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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 205350dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.e1 | 205350dm1 | \([1, 1, 0, -2242450, -547293500]\) | \(908905/432\) | \(592730907849168750000\) | \([]\) | \(11508480\) | \(2.6799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350dm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 205350dm do not have complex multiplication.Modular form 205350.2.a.dm
sage: E.q_eigenform(10)