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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 106722dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.k1 | 106722dt1 | \([1, -1, 0, -45331281, -117618118227]\) | \(-4631003113/7056\) | \(-15696441005922632639376\) | \([]\) | \(16220160\) | \(3.1589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722dt1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106722dt do not have complex multiplication.Modular form 106722.2.a.dt
sage: E.q_eigenform(10)