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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 54096x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.w1 | 54096x1 | \([0, -1, 0, -33728, -2379264]\) | \(-179706625/552\) | \(-13034168942592\) | \([]\) | \(169344\) | \(1.3849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54096x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 54096x do not have complex multiplication.Modular form 54096.2.a.x
sage: E.q_eigenform(10)