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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1638.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1638.k1 | 1638r1 | \([1, -1, 1, -41477, -3246595]\) | \(-10824513276632329/21926008832\) | \(-15984060438528\) | \([]\) | \(9240\) | \(1.4205\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1638.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1638.k do not have complex multiplication.Modular form 1638.2.a.k
sage: E.q_eigenform(10)