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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 32192.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32192.k1 | 32192d1 | \([0, -1, 0, -2017, -34207]\) | \(-3463512697/503\) | \(-131858432\) | \([]\) | \(11264\) | \(0.57299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32192.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 32192.k do not have complex multiplication.Modular form 32192.2.a.k
sage: E.q_eigenform(10)