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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 12600w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12600.cn1 | 12600w1 | \([0, 0, 0, -300, -15500]\) | \(-1024/35\) | \(-102060000000\) | \([]\) | \(11520\) | \(0.79269\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12600w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12600w do not have complex multiplication.Modular form 12600.2.a.w
sage: E.q_eigenform(10)