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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 75690j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75690.j1 | 75690j1 | \([1, -1, 0, -1361038815, -14503447037619]\) | \(764581408291686481/193273528320000\) | \(70482919772286865196974080000\) | \([]\) | \(77952000\) | \(4.2452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75690j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75690j do not have complex multiplication.Modular form 75690.2.a.j
sage: E.q_eigenform(10)