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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1216.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1216.p1 | 1216g1 | \([0, -1, 0, -5, 29]\) | \(-1024/19\) | \(-311296\) | \([]\) | \(128\) | \(-0.26491\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1216.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1216.p do not have complex multiplication.Modular form 1216.2.a.p
sage: E.q_eigenform(10)