Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 36414.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36414.bw1 | 36414ck2 | \([1, -1, 1, -992336, -380181013]\) | \(6141556990297/1019592\) | \(17941034271597192\) | \([2]\) | \(442368\) | \(2.1268\) | |
| 36414.bw2 | 36414ck1 | \([1, -1, 1, -55976, -7135189]\) | \(-1102302937/616896\) | \(-10855079559285696\) | \([2]\) | \(221184\) | \(1.7802\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36414.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 36414.bw do not have complex multiplication.Modular form 36414.2.a.bw
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.
