Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 6240.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6240.ba1 | 6240s2 | \([0, 1, 0, -1320, -18900]\) | \(497169541448/190125\) | \(97344000\) | \([2]\) | \(3840\) | \(0.49873\) | |
| 6240.ba2 | 6240s1 | \([0, 1, 0, -70, -400]\) | \(-601211584/609375\) | \(-39000000\) | \([2]\) | \(1920\) | \(0.15216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6240.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 6240.ba do not have complex multiplication.Modular form 6240.2.a.ba
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
