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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 224400df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.z1 | 224400df1 | \([0, -1, 0, 115752, 12202992]\) | \(334992828740851/320302743552\) | \(-163995004698624000\) | \([]\) | \(1838592\) | \(1.9903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 224400df1 has rank \(1\).
Complex multiplication
The elliptic curves in class 224400df do not have complex multiplication.Modular form 224400.2.a.df
sage: E.q_eigenform(10)