Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 58800.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.c1 | 58800gi3 | \([0, -1, 0, -369133, -79606988]\) | \(189123395584/16078125\) | \(472893832031250000\) | \([2]\) | \(995328\) | \(2.1329\) | |
| 58800.c2 | 58800gi1 | \([0, -1, 0, -75133, 7931512]\) | \(1594753024/4725\) | \(138972881250000\) | \([2]\) | \(331776\) | \(1.5836\) | \(\Gamma_0(N)\)-optimal |
| 58800.c3 | 58800gi2 | \([0, -1, 0, -44508, 14424012]\) | \(-20720464/178605\) | \(-84050798580000000\) | \([2]\) | \(663552\) | \(1.9301\) | |
| 58800.c4 | 58800gi4 | \([0, -1, 0, 396492, -367481988]\) | \(14647977776/132355125\) | \(-62285792404500000000\) | \([2]\) | \(1990656\) | \(2.4795\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.c have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.c do not have complex multiplication.Modular form 58800.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
