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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 49686.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49686.w1 | 49686n1 | \([1, 1, 0, 49514, -4124882]\) | \(68921/78\) | \(-15192773969104914\) | \([]\) | \(376320\) | \(1.7914\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49686.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 49686.w do not have complex multiplication.Modular form 49686.2.a.w
sage: E.q_eigenform(10)