Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 13860.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.l1 | 13860q2 | \([0, 0, 0, -1263, 3638]\) | \(1193895376/660275\) | \(123223161600\) | \([2]\) | \(13824\) | \(0.81860\) | |
| 13860.l2 | 13860q1 | \([0, 0, 0, -768, -8143]\) | \(4294967296/29645\) | \(345779280\) | \([2]\) | \(6912\) | \(0.47203\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.l have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.l do not have complex multiplication.Modular form 13860.2.a.l
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.
