Show commands:
SageMath
E = EllipticCurve("je1")
E.isogeny_class()
Elliptic curves in class 286650je
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.je2 | 286650je1 | \([1, -1, 1, 7871620, -96047218753]\) | \(40251338884511/2997011332224\) | \(-4016281821217105986000000\) | \([]\) | \(63221760\) | \(3.4006\) | \(\Gamma_0(N)\)-optimal |
| 286650.je1 | 286650je2 | \([1, -1, 1, -40511318630, -3138421580407753]\) | \(-5486773802537974663600129/2635437714\) | \(-3531738591670115531250\) | \([]\) | \(442552320\) | \(4.3735\) |
Rank
sage: E.rank()
The elliptic curves in class 286650je have rank \(0\).
Complex multiplication
The elliptic curves in class 286650je do not have complex multiplication.Modular form 286650.2.a.je
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
