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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 5586.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5586.m1 | 5586m1 | \([1, 0, 1, 3200311, 1766681228]\) | \(628805222251722551/597713542447104\) | \(-3445699627212607586304\) | \([]\) | \(395136\) | \(2.8198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5586.m1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5586.m do not have complex multiplication.Modular form 5586.2.a.m
sage: E.q_eigenform(10)