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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 27225p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27225.d1 | 27225p1 | \([0, 0, 1, -7425, -250594]\) | \(-1216512/25\) | \(-930329296875\) | \([]\) | \(69120\) | \(1.0881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27225p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 27225p do not have complex multiplication.Modular form 27225.2.a.p
sage: E.q_eigenform(10)