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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 121242.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121242.x1 | 121242bb1 | \([1, 1, 1, -66008, -6555031]\) | \(-17953855881625/264528\) | \(-468627488208\) | \([]\) | \(506880\) | \(1.3771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 121242.x do not have complex multiplication.Modular form 121242.2.a.x
sage: E.q_eigenform(10)