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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 11466cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11466.bo3 | 11466cb1 | \([1, -1, 1, -24926, -1466643]\) | \(19968681097/628992\) | \(53946203980032\) | \([2]\) | \(36864\) | \(1.4098\) | \(\Gamma_0(N)\)-optimal |
| 11466.bo2 | 11466cb2 | \([1, -1, 1, -60206, 3641901]\) | \(281397674377/96589584\) | \(8284113948683664\) | \([2, 2]\) | \(73728\) | \(1.7563\) | |
| 11466.bo1 | 11466cb3 | \([1, -1, 1, -862826, 308637501]\) | \(828279937799497/193444524\) | \(16590986452171404\) | \([2]\) | \(147456\) | \(2.1029\) | |
| 11466.bo4 | 11466cb4 | \([1, -1, 1, 177934, 25169757]\) | \(7264187703863/7406095788\) | \(-635192107491198348\) | \([2]\) | \(147456\) | \(2.1029\) |
Rank
sage: E.rank()
The elliptic curves in class 11466cb have rank \(0\).
Complex multiplication
The elliptic curves in class 11466cb do not have complex multiplication.Modular form 11466.2.a.cb
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.
