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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 104742x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104742.v1 | 104742x1 | \([1, -1, 0, -306, -2700]\) | \(-8231953/3872\) | \(-1493201952\) | \([]\) | \(57600\) | \(0.46637\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 104742x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 104742x do not have complex multiplication.Modular form 104742.2.a.x
sage: E.q_eigenform(10)