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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 98736.cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.cm1 | 98736dn1 | \([0, 1, 0, -7219989, -7469535933]\) | \(-5736108018368512/11042163\) | \(-80125400377110528\) | \([]\) | \(2764800\) | \(2.4974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 98736.cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 98736.cm do not have complex multiplication.Modular form 98736.2.a.cm
sage: E.q_eigenform(10)