Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5520.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.z1 | 5520y2 | \([0, 1, 0, -1856, -30156]\) | \(172715635009/7935000\) | \(32501760000\) | \([2]\) | \(4608\) | \(0.77868\) | |
| 5520.z2 | 5520y1 | \([0, 1, 0, 64, -1740]\) | \(6967871/331200\) | \(-1356595200\) | \([2]\) | \(2304\) | \(0.43211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.z have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.z do not have complex multiplication.Modular form 5520.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
