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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 340704cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 340704.cj2 | 340704cj1 | \([0, 0, 0, 2535, 272428]\) | \(8000/147\) | \(-33104341303488\) | \([2]\) | \(589824\) | \(1.2747\) | \(\Gamma_0(N)\)-optimal |
| 340704.cj1 | 340704cj2 | \([0, 0, 0, -50700, 4147936]\) | \(1000000/63\) | \(908004790038528\) | \([2]\) | \(1179648\) | \(1.6212\) |
Rank
sage: E.rank()
The elliptic curves in class 340704cj have rank \(1\).
Complex multiplication
The elliptic curves in class 340704cj do not have complex multiplication.Modular form 340704.2.a.cj
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.
