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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 19950.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19950.k1 | 19950c1 | \([1, 1, 0, -4759164375, 40711823733367125]\) | \(-762949514912708039797646866801/45824812197620141357267649822720\) | \(-716012690587814708707307028480000000\) | \([]\) | \(356590080\) | \(5.5588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19950.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19950.k do not have complex multiplication.Modular form 19950.2.a.k
sage: E.q_eigenform(10)