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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 121275.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.z1 | 121275eu1 | \([0, 0, 1, -19234425, -32153108094]\) | \(1409995418369929216/15792626953125\) | \(8814506678009033203125\) | \([]\) | \(12165120\) | \(3.0248\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121275.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121275.z do not have complex multiplication.Modular form 121275.2.a.z
sage: E.q_eigenform(10)