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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 369600iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.iz3 | 369600iz1 | \([0, -1, 0, -317469633, -2171689228863]\) | \(863913648706111516969/2486234429521920\) | \(10183616223321784320000000\) | \([2]\) | \(115605504\) | \(3.6696\) | \(\Gamma_0(N)\)-optimal |
| 369600.iz2 | 369600iz2 | \([0, -1, 0, -448541633, -207575308863]\) | \(2436531580079063806249/1405478914998681600\) | \(5756841635834599833600000000\) | \([2, 2]\) | \(231211008\) | \(4.0162\) | |
| 369600.iz1 | 369600iz3 | \([0, -1, 0, -4785181633, 126947046131137]\) | \(2958414657792917260183849/12401051653985258880\) | \(50794707574723620372480000000\) | \([2]\) | \(462422016\) | \(4.3628\) | |
| 369600.iz4 | 369600iz4 | \([0, -1, 0, 1790946367, -1661003020863]\) | \(155099895405729262880471/90047655797243760000\) | \(-368835198145510440960000000000\) | \([2]\) | \(462422016\) | \(4.3628\) |
Rank
sage: E.rank()
The elliptic curves in class 369600iz have rank \(0\).
Complex multiplication
The elliptic curves in class 369600iz do not have complex multiplication.Modular form 369600.2.a.iz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
