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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 18032k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18032.i1 | 18032k1 | \([0, -1, 0, -212, 1303]\) | \(-562432/23\) | \(-43294832\) | \([]\) | \(4608\) | \(0.23284\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 18032k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 18032k do not have complex multiplication.Modular form 18032.2.a.k
sage: E.q_eigenform(10)