Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 10608.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.n1 | 10608f1 | \([0, 1, 0, -424, 3140]\) | \(8251733668/232713\) | \(238298112\) | \([2]\) | \(7168\) | \(0.38624\) | \(\Gamma_0(N)\)-optimal |
| 10608.n2 | 10608f2 | \([0, 1, 0, 96, 10836]\) | \(47279806/24649677\) | \(-50482538496\) | \([2]\) | \(14336\) | \(0.73281\) |
Rank
sage: E.rank()
The elliptic curves in class 10608.n have rank \(2\).
Complex multiplication
The elliptic curves in class 10608.n do not have complex multiplication.Modular form 10608.2.a.n
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.
