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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 112710.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
112710.w1 | 112710be1 | \([1, 0, 1, -1749, 113272]\) | \(-2045682844201/18044839800\) | \(-5214958702200\) | \([]\) | \(280800\) | \(1.1228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710.w do not have complex multiplication.Modular form 112710.2.a.w
sage: E.q_eigenform(10)