Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 51984.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51984.ca1 | 51984cp1 | \([0, 0, 0, -69312, 7051052]\) | \(-4194304/19\) | \(-166817919419136\) | \([]\) | \(207360\) | \(1.5806\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51984.ca1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51984.ca do not have complex multiplication.Modular form 51984.2.a.ca
sage: E.q_eigenform(10)