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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 242760.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242760.w1 | 242760w1 | \([0, -1, 0, -219056, 40040700]\) | \(-3928197859398724/58604765625\) | \(-17343259920000000\) | \([]\) | \(2032128\) | \(1.9195\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 242760.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 242760.w do not have complex multiplication.Modular form 242760.2.a.w
sage: E.q_eigenform(10)