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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 23232cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23232.ca1 | 23232cm1 | \([0, 1, 0, 15, 9]\) | \(45056/27\) | \(-209088\) | \([]\) | \(2880\) | \(-0.28984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 23232cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 23232cm do not have complex multiplication.Modular form 23232.2.a.cm
sage: E.q_eigenform(10)