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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 116886.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116886.m1 | 116886l6 | \([1, 0, 1, -8334128377, 292844688915986]\) | \(36136672427711016379227705697/1011258101510224722\) | \(1791505413569555218731042\) | \([2]\) | \(98304000\) | \(4.1645\) | |
| 116886.m2 | 116886l4 | \([1, 0, 1, -596424007, -5595437019394]\) | \(13244420128496241770842177/29965867631164664892\) | \(53086362426533704900736412\) | \([2]\) | \(49152000\) | \(3.8180\) | |
| 116886.m3 | 116886l3 | \([1, 0, 1, -521544367, 4563463980590]\) | \(8856076866003496152467137/46664863048067576004\) | \(82669651446297643013222244\) | \([2, 2]\) | \(49152000\) | \(3.8180\) | |
| 116886.m4 | 116886l5 | \([1, 0, 1, -239264677, 9484050624794]\) | \(-855073332201294509246497/21439133060285771735058\) | \(-37980732003412922060731085538\) | \([2]\) | \(98304000\) | \(4.1645\) | |
| 116886.m5 | 116886l2 | \([1, 0, 1, -50900347, -17784910090]\) | \(8232463578739844255617/4687062591766850064\) | \(8303417292133072666229904\) | \([2, 2]\) | \(24576000\) | \(3.4714\) | |
| 116886.m6 | 116886l1 | \([1, 0, 1, 12610133, -2212140394]\) | \(125177609053596564863/73635189229502208\) | \(-130449229466606161106688\) | \([2]\) | \(12288000\) | \(3.1248\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.m have rank \(1\).
Complex multiplication
The elliptic curves in class 116886.m do not have complex multiplication.Modular form 116886.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
