Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 106722w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.dh1 | 106722w1 | \([1, -1, 0, -160857846, 785501859764]\) | \(-34068278205171/10307264\) | \(-139265542422918501936192\) | \([]\) | \(16934400\) | \(3.4185\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 106722w do not have complex multiplication.Modular form 106722.2.a.w
sage: E.q_eigenform(10)