Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 7488.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.r1 | 7488g2 | \([0, 0, 0, -1836, -20304]\) | \(530604/169\) | \(218000719872\) | \([2]\) | \(6144\) | \(0.87944\) | |
| 7488.r2 | 7488g1 | \([0, 0, 0, 324, -2160]\) | \(11664/13\) | \(-4192321536\) | \([2]\) | \(3072\) | \(0.53286\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.r have rank \(0\).
Complex multiplication
The elliptic curves in class 7488.r do not have complex multiplication.Modular form 7488.2.a.r
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.
