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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 104742.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104742.k1 | 104742t1 | \([1, -1, 0, -314325, -63159021]\) | \(31824875809/2409066\) | \(259981977460892346\) | \([]\) | \(1216512\) | \(2.0867\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 104742.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 104742.k do not have complex multiplication.Modular form 104742.2.a.k
sage: E.q_eigenform(10)