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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 51520.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51520.w1 | 51520bh1 | \([0, -1, 0, -805, -9475]\) | \(-3525581824/462875\) | \(-7583744000\) | \([]\) | \(27648\) | \(0.62878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51520.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51520.w do not have complex multiplication.Modular form 51520.2.a.w
sage: E.q_eigenform(10)