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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 53312.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.f1 | 53312bg1 | \([0, 0, 0, -67228, 6722800]\) | \(-7260624/17\) | \(-78677266153472\) | \([]\) | \(516096\) | \(1.5468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 53312.f do not have complex multiplication.Modular form 53312.2.a.f
sage: E.q_eigenform(10)