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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 12789p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12789.o1 | 12789p1 | \([0, 0, 1, -273, 1125]\) | \(62992384/21141\) | \(755177661\) | \([]\) | \(8064\) | \(0.40601\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12789p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12789p do not have complex multiplication.Modular form 12789.2.a.p
sage: E.q_eigenform(10)