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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 32340w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.x1 | 32340w1 | \([0, 1, 0, -506, -1396431]\) | \(-373698304/21923067375\) | \(-842196556278000\) | \([]\) | \(120960\) | \(1.5428\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32340w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 32340w do not have complex multiplication.Modular form 32340.2.a.w
sage: E.q_eigenform(10)