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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 361998x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361998.x1 | 361998x1 | \([1, -1, 0, -284534262, -2753961856268]\) | \(-724002020651148891625/512198939204813952\) | \(-1802296821717757394765753472\) | \([]\) | \(154893312\) | \(3.9299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 361998x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 361998x do not have complex multiplication.Modular form 361998.2.a.x
sage: E.q_eigenform(10)