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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 338130.df
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.df1 | 338130df1 | \([1, -1, 1, -9668, -500633]\) | \(-1033364331/532480\) | \(-51492189265920\) | \([]\) | \(1437696\) | \(1.3356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 338130.df1 has rank \(1\).
Complex multiplication
The elliptic curves in class 338130.df do not have complex multiplication.Modular form 338130.2.a.df
sage: E.q_eigenform(10)