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SageMath
E = EllipticCurve("hm1")
E.isogeny_class()
Elliptic curves in class 117600.hm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.hm1 | 117600da1 | \([0, 1, 0, -91408, -10667812]\) | \(-215474070728/3645\) | \(-1428840000000\) | \([]\) | \(304128\) | \(1.4624\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117600.hm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 117600.hm do not have complex multiplication.Modular form 117600.2.a.hm
sage: E.q_eigenform(10)