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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 39039k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39039.y1 | 39039k1 | \([0, -1, 1, 318002, -72779445]\) | \(736803680768000/899079608427\) | \(-4339685545671919443\) | \([]\) | \(1100736\) | \(2.2623\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39039k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 39039k do not have complex multiplication.Modular form 39039.2.a.k
sage: E.q_eigenform(10)