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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 106722o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.d1 | 106722o1 | \([1, -1, 0, -36145104, 84079049984]\) | \(-705703720113/4194304\) | \(-31039138065002746871808\) | \([]\) | \(20756736\) | \(3.1560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722o1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106722o do not have complex multiplication.Modular form 106722.2.a.o
sage: E.q_eigenform(10)