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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 19600.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.w1 | 19600cv1 | \([0, 1, 0, -2858, 58183]\) | \(-160000\) | \(-16141442800\) | \([]\) | \(16128\) | \(0.79680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19600.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19600.w do not have complex multiplication.Modular form 19600.2.a.w
sage: E.q_eigenform(10)