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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 177870.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177870.w1 | 177870je1 | \([1, 1, 0, 1778577, -909128667]\) | \(4161311/4800\) | \(-717715638130893124800\) | \([]\) | \(10378368\) | \(2.6882\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177870.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 177870.w do not have complex multiplication.Modular form 177870.2.a.w
sage: E.q_eigenform(10)