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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 76440.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.x1 | 76440bz1 | \([0, -1, 0, -124280, -16822308]\) | \(-35962234084/195\) | \(-1151115463680\) | \([]\) | \(303744\) | \(1.5084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 76440.x do not have complex multiplication.Modular form 76440.2.a.x
sage: E.q_eigenform(10)