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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4312.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4312.h1 | 4312g1 | \([0, 1, 0, -65, -67453]\) | \(-1024/65219\) | \(-1964275233536\) | \([]\) | \(4608\) | \(1.0377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4312.h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4312.h do not have complex multiplication.Modular form 4312.2.a.h
sage: E.q_eigenform(10)