Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 170352.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.bl1 | 170352y3 | \([0, 0, 0, -47613891, 126433153730]\) | \(828279937799497/193444524\) | \(2788072292043222073344\) | \([2]\) | \(12386304\) | \(3.1056\) | |
| 170352.bl2 | 170352y2 | \([0, 0, 0, -3322371, 1486775810]\) | \(281397674377/96589584\) | \(1392123887933789896704\) | \([2, 2]\) | \(6193152\) | \(2.7590\) | |
| 170352.bl3 | 170352y1 | \([0, 0, 0, -1375491, -603783934]\) | \(19968681097/628992\) | \(9065519823744663552\) | \([2]\) | \(3096576\) | \(2.4124\) | \(\Gamma_0(N)\)-optimal |
| 170352.bl4 | 170352y4 | \([0, 0, 0, 9819069, 10336221506]\) | \(7264187703863/7406095788\) | \(-106742388110923279024128\) | \([2]\) | \(12386304\) | \(3.1056\) |
Rank
sage: E.rank()
The elliptic curves in class 170352.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 170352.bl do not have complex multiplication.Modular form 170352.2.a.bl
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.
