Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 106560.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.o1 | 106560cg4 | \([0, 0, 0, -206391230508, 36089841446003248]\) | \(5087799435928552778197163696329/125914832087040\) | \(24062699134373635031040\) | \([2]\) | \(302776320\) | \(4.7402\) | |
| 106560.o2 | 106560cg2 | \([0, 0, 0, -12899467308, 563902358725168]\) | \(1242142983306846366056931529/6179359141291622400\) | \(1180893921673633524508262400\) | \([2, 2]\) | \(151388160\) | \(4.3936\) | |
| 106560.o3 | 106560cg3 | \([0, 0, 0, -12681232428, 583902887125552]\) | \(-1180159344892952613848670409/87759036144023189760000\) | \(-16771012978014396176148725760000\) | \([2]\) | \(302776320\) | \(4.7402\) | |
| 106560.o4 | 106560cg1 | \([0, 0, 0, -819871788, 8497052230192]\) | \(318929057401476905525449/21353131537921474560\) | \(4080646983816250642724290560\) | \([2]\) | \(75694080\) | \(4.0471\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106560.o have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.o do not have complex multiplication.Modular form 106560.2.a.o
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
