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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 134640.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.w1 | 134640dr1 | \([0, 0, 0, 281277, -157286078]\) | \(22253722294800933/109514680000000\) | \(-12111447490560000000\) | \([]\) | \(2419200\) | \(2.3440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 134640.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 134640.w do not have complex multiplication.Modular form 134640.2.a.w
sage: E.q_eigenform(10)