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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 252700.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
252700.w1 | 252700w1 | \([0, 0, 0, -45125, -4286875]\) | \(-34560/7\) | \(-2058257293750000\) | \([]\) | \(1179360\) | \(1.6609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 252700.w1 has rank \(2\).
Complex multiplication
The elliptic curves in class 252700.w do not have complex multiplication.Modular form 252700.2.a.w
sage: E.q_eigenform(10)