Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 48510ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.dv4 | 48510ci1 | \([1, -1, 1, 12853, -2591781]\) | \(73929353373/954060800\) | \(-3030596074598400\) | \([2]\) | \(331776\) | \(1.6514\) | \(\Gamma_0(N)\)-optimal |
| 48510.dv2 | 48510ci2 | \([1, -1, 1, -222347, -37683621]\) | \(382704614800227/27778076480\) | \(88237698834479040\) | \([2]\) | \(663552\) | \(1.9980\) | |
| 48510.dv3 | 48510ci3 | \([1, -1, 1, -116507, 72764731]\) | \(-75526045083/943250000\) | \(-2184270128097750000\) | \([2]\) | \(995328\) | \(2.2007\) | |
| 48510.dv1 | 48510ci4 | \([1, -1, 1, -3424007, 2431673731]\) | \(1917114236485083/7117764500\) | \(16482502386625621500\) | \([2]\) | \(1990656\) | \(2.5473\) |
Rank
sage: E.rank()
The elliptic curves in class 48510ci have rank \(1\).
Complex multiplication
The elliptic curves in class 48510ci do not have complex multiplication.Modular form 48510.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
