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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 250470w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250470.w1 | 250470w1 | \([1, -1, 0, -32944995, 2474274325]\) | \(209140276356121/120891312000\) | \(2285859172348739587248000\) | \([]\) | \(42577920\) | \(3.3636\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 250470w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 250470w do not have complex multiplication.Modular form 250470.2.a.w
sage: E.q_eigenform(10)