Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 95139.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95139.c1 | 95139j4 | \([1, -1, 1, -1267259, 548870600]\) | \(347873904937/395307\) | \(255759748448673843\) | \([2]\) | \(1382400\) | \(2.2537\) | |
| 95139.c2 | 95139j2 | \([1, -1, 1, -99644, 3827918]\) | \(169112377/88209\) | \(57070357091852841\) | \([2, 2]\) | \(691200\) | \(1.9071\) | |
| 95139.c3 | 95139j1 | \([1, -1, 1, -56399, -5097850]\) | \(30664297/297\) | \(192156084484353\) | \([2]\) | \(345600\) | \(1.5605\) | \(\Gamma_0(N)\)-optimal |
| 95139.c4 | 95139j3 | \([1, -1, 1, 376051, 29515448]\) | \(9090072503/5845851\) | \(-3782208210905520099\) | \([2]\) | \(1382400\) | \(2.2537\) |
Rank
sage: E.rank()
The elliptic curves in class 95139.c have rank \(0\).
Complex multiplication
The elliptic curves in class 95139.c do not have complex multiplication.Modular form 95139.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
