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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 46410.cn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.cn1 | 46410cm6 | \([1, 0, 0, -73322765620, -7595474963359738]\) | \(43595355616903186726969048523604598081/306218213075771927833557128906250\) | \(306218213075771927833557128906250\) | \([2]\) | \(270532608\) | \(5.0663\) | |
| 46410.cn2 | 46410cm4 | \([1, 0, 0, -7562905090, 54672107453600]\) | \(47839833887939781795850621588688161/26393794292755443609008789062500\) | \(26393794292755443609008789062500\) | \([2, 2]\) | \(135266304\) | \(4.7198\) | |
| 46410.cn3 | 46410cm2 | \([1, 0, 0, -5766634510, 168310291664372]\) | \(21207574048850823872792738495132641/34982717474287728110306250000\) | \(34982717474287728110306250000\) | \([2, 4]\) | \(67633152\) | \(4.3732\) | |
| 46410.cn4 | 46410cm1 | \([1, 0, 0, -5764349630, 168450516120900]\) | \(21182375175311718755156119308023521/57778579333189522080000\) | \(57778579333189522080000\) | \([8]\) | \(33816576\) | \(4.0266\) | \(\Gamma_0(N)\)-optimal |
| 46410.cn5 | 46410cm3 | \([1, 0, 0, -4006922010, 272974119796872]\) | \(-7114696532582636527413245800532641/28073201392582203302585928742500\) | \(-28073201392582203302585928742500\) | \([4]\) | \(135266304\) | \(4.7198\) | |
| 46410.cn6 | 46410cm5 | \([1, 0, 0, 29456626160, 431982573859850]\) | \(2826654455041045345083039379223811839/1716409549902715755405793403906250\) | \(-1716409549902715755405793403906250\) | \([2]\) | \(270532608\) | \(5.0663\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 46410.cn do not have complex multiplication.Modular form 46410.2.a.cn
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
