Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 13860.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13860.s1 | 13860v2 | \([0, 0, 0, -21432, 3317956]\) | \(-5833703071744/22107421875\) | \(-4125775500000000\) | \([3]\) | \(62208\) | \(1.6819\) | |
| 13860.s2 | 13860v1 | \([0, 0, 0, 2328, -108236]\) | \(7476617216/31444875\) | \(-5868368352000\) | \([]\) | \(20736\) | \(1.1326\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13860.s have rank \(1\).
Complex multiplication
The elliptic curves in class 13860.s do not have complex multiplication.Modular form 13860.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
