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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 15600.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15600.k1 | 15600bg1 | \([0, -1, 0, -13208, -580368]\) | \(-2488672890625/2426112\) | \(-248433868800\) | \([]\) | \(27648\) | \(1.1072\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15600.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 15600.k do not have complex multiplication.Modular form 15600.2.a.k
sage: E.q_eigenform(10)