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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1728k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.ba1 | 1728k1 | \([0, 0, 0, -48, 160]\) | \(-3072\) | \(-3981312\) | \([]\) | \(384\) | \(-0.021022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1728k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1728k do not have complex multiplication.Modular form 1728.2.a.k
sage: E.q_eigenform(10)