Show commands:
SageMath
E = EllipticCurve("js1")
E.isogeny_class()
Elliptic curves in class 78400.js
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.js1 | 78400ib2 | \([0, -1, 0, -197633, -33344863]\) | \(3543122/49\) | \(11806312448000000\) | \([2]\) | \(491520\) | \(1.8896\) | |
| 78400.js2 | 78400ib1 | \([0, -1, 0, -1633, -1396863]\) | \(-4/7\) | \(-843308032000000\) | \([2]\) | \(245760\) | \(1.5430\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.js have rank \(1\).
Complex multiplication
The elliptic curves in class 78400.js do not have complex multiplication.Modular form 78400.2.a.js
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.
