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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 1728.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.s1 | 1728b1 | \([0, 0, 0, -12, -272]\) | \(-6\) | \(-31850496\) | \([]\) | \(384\) | \(0.11906\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1728.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1728.s do not have complex multiplication.Modular form 1728.2.a.s
sage: E.q_eigenform(10)