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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 75712.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.j1 | 75712bj1 | \([0, 1, 0, -38081, -3786977]\) | \(-114244/49\) | \(-2619526698041344\) | \([]\) | \(399360\) | \(1.6660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75712.j do not have complex multiplication.Modular form 75712.2.a.j
sage: E.q_eigenform(10)