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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 364650.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364650.ci1 | 364650ci4 | \([1, 0, 1, -62741328601, -6048934264659652]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(13870228131645035363928000000\) | \([2]\) | \(1210318848\) | \(4.7327\) | |
| 364650.ci2 | 364650ci3 | \([1, 0, 1, -8582608601, 168305381804348]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(28223880577421789053927848000000\) | \([2]\) | \(1210318848\) | \(4.7327\) | |
| 364650.ci3 | 364650ci2 | \([1, 0, 1, -3942544601, -93440628435652]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(150189410472185661198336000000\) | \([2, 2]\) | \(605159424\) | \(4.3861\) | |
| 364650.ci4 | 364650ci1 | \([1, 0, 1, 22383399, -4475573971652]\) | \(79374649975090937760383/553856914190911653543936\) | \(-8654014284232994586624000000\) | \([2]\) | \(302579712\) | \(4.0396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 364650.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 364650.ci do not have complex multiplication.Modular form 364650.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
