Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 57960.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57960.v1 | 57960r6 | \([0, 0, 0, -12799443, 17625225742]\) | \(155324313723954725282/13018359375\) | \(19436306400000000\) | \([2]\) | \(1835008\) | \(2.5680\) | |
| 57960.v2 | 57960r4 | \([0, 0, 0, -1101603, -444555218]\) | \(198048499826486404/242568272835\) | \(181076245398236160\) | \([2]\) | \(917504\) | \(2.2214\) | |
| 57960.v3 | 57960r3 | \([0, 0, 0, -801723, 274123078]\) | \(76343005935514084/694180580625\) | \(518203026714240000\) | \([2, 2]\) | \(917504\) | \(2.2214\) | |
| 57960.v4 | 57960r5 | \([0, 0, 0, -234723, 654353278]\) | \(-957928673903042/123339801817575\) | \(-184145337395224934400\) | \([2]\) | \(1835008\) | \(2.5680\) | |
| 57960.v5 | 57960r2 | \([0, 0, 0, -87303, -2928998]\) | \(394315384276816/208332909225\) | \(38879920851206400\) | \([2, 2]\) | \(458752\) | \(1.8748\) | |
| 57960.v6 | 57960r1 | \([0, 0, 0, 20742, -357527]\) | \(84611246065664/53699121315\) | \(-626346551018160\) | \([2]\) | \(229376\) | \(1.5282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57960.v have rank \(0\).
Complex multiplication
The elliptic curves in class 57960.v do not have complex multiplication.Modular form 57960.2.a.v
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.
