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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 450072j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450072.j1 | 450072j1 | \([0, 0, 0, -318, 2221]\) | \(-304900096/6251\) | \(-72911664\) | \([]\) | \(115200\) | \(0.30035\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450072j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 450072j do not have complex multiplication.Modular form 450072.2.a.j
sage: E.q_eigenform(10)