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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 83490.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83490.k1 | 83490o1 | \([1, 1, 0, -22550772, 41208919536]\) | \(5916522263654774761/134323680\) | \(28793473736602080\) | \([]\) | \(3970560\) | \(2.6822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83490.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 83490.k do not have complex multiplication.Modular form 83490.2.a.k
sage: E.q_eigenform(10)