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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 179520.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.cm1 | 179520gt1 | \([0, -1, 0, -5884065, -14898985695]\) | \(-85944135790429956649/316171526414008320\) | \(-82882468620273797038080\) | \([]\) | \(14100480\) | \(3.0834\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 179520.cm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 179520.cm do not have complex multiplication.Modular form 179520.2.a.cm
sage: E.q_eigenform(10)