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SageMath
E = EllipticCurve("jk1")
E.isogeny_class()
Elliptic curves in class 366912jk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.jk2 | 366912jk1 | \([0, 0, 0, -144795, -21194656]\) | \(61162984000/41067\) | \(225418066630848\) | \([2]\) | \(1843200\) | \(1.6925\) | \(\Gamma_0(N)\)-optimal |
| 366912.jk1 | 366912jk2 | \([0, 0, 0, -173460, -12205312]\) | \(1643032000/767637\) | \(269669367095611392\) | \([2]\) | \(3686400\) | \(2.0391\) |
Rank
sage: E.rank()
The elliptic curves in class 366912jk have rank \(1\).
Complex multiplication
The elliptic curves in class 366912jk do not have complex multiplication.Modular form 366912.2.a.jk
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 Cremona 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 Cremona labels.
