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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 20449e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20449.b1 | 20449e1 | \([1, 1, 1, -388957, -58947426]\) | \(6289657/2197\) | \(2273168619161481613\) | \([]\) | \(266112\) | \(2.2238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20449e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 20449e do not have complex multiplication.Modular form 20449.2.a.e
sage: E.q_eigenform(10)