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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 412224w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.w1 | 412224w1 | \([0, -1, 0, 3915, 22599]\) | \(103664033202176/63847694259\) | \(-4086252432576\) | \([]\) | \(746496\) | \(1.1090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 412224w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 412224w do not have complex multiplication.Modular form 412224.2.a.w
sage: E.q_eigenform(10)