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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 68400.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68400.x1 | 68400bo1 | \([0, 0, 0, -159375, -12659375]\) | \(3930400000/1666737\) | \(189851761406250000\) | \([]\) | \(691200\) | \(2.0121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68400.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 68400.x do not have complex multiplication.Modular form 68400.2.a.x
sage: E.q_eigenform(10)