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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 112710.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.v1 | 112710z1 | \([1, 0, 1, 1769396, -684735094]\) | \(87822908801351/79872000000\) | \(-557167698327552000000\) | \([]\) | \(4744224\) | \(2.6681\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710.v1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710.v do not have complex multiplication.Modular form 112710.2.a.v
sage: E.q_eigenform(10)