What question did this study set out to answer?

The research investigates the relationship between the number of integer solutions to a quadratic form and the point-counting of elliptic curves over finite fields.

February 19, 2026The Ramanujan JournalOpen Access

Relating elliptic curve point-counting and solutions of quadratic forms with congruence conditions

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The research investigates the relationship between the number of integer solutions to a quadratic form and the point-counting of elliptic curves over finite fields.
Analyzed theta series related to the quadratic form.
Applied operators on modular, non-holomorphic Eisenstein series of weight 2.
Constructed a basis for Eisenstein space at specific levels, including powers of 2 and 3.
Examined the connection between the trace of Frobenius on elliptic curves and Fourier coefficients of cusp forms.
Established a relationship between integer solutions of the quadratic form and the number of rational points on elliptic curves under congruence conditions.
Identified specific cases for prime moduli and congruences to enhance understanding of the point-counting problem.

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Implication

Analysis reveals connections between elliptic curves and quadratic forms, indicating deeper number theory implications.

Cite This Study

Koustav Mondal (2026) studied this question.

synapsesocial.com/papers/6996a77aecb39a600b3ed19d https://doi.org/10.1007/s11139-026-01341-5

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Relating elliptic curve point-counting and solutions of quadratic forms with congruence conditions

Key Points

Discussion

Implication

Cite This Study

Relating elliptic curve point-counting and solutions of quadratic forms with congruence conditions

Key Points

Discussion

Implication

Cite This Study

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