Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 134640.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.ba1 | 134640dy2 | \([0, 0, 0, -738963, -244497582]\) | \(553529221679043/11190080\) | \(902161795645440\) | \([2]\) | \(1105920\) | \(1.9899\) | |
| 134640.ba2 | 134640dy1 | \([0, 0, 0, -47763, -3545262]\) | \(149467669443/19148800\) | \(1543806281318400\) | \([2]\) | \(552960\) | \(1.6433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134640.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 134640.ba do not have complex multiplication.Modular form 134640.2.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.
