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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 392784.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.s1 | 392784s1 | \([0, -1, 0, -5553, 188973]\) | \(-30814336000/6777027\) | \(-4165540307712\) | \([]\) | \(493440\) | \(1.1421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 392784.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 392784.s do not have complex multiplication.Modular form 392784.2.a.s
sage: E.q_eigenform(10)