Show commands:
SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 66240eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.bm2 | 66240eu1 | \([0, 0, 0, 77172, -8504048]\) | \(265971760991/317400000\) | \(-60656084582400000\) | \([2]\) | \(368640\) | \(1.9066\) | \(\Gamma_0(N)\)-optimal |
| 66240.bm1 | 66240eu2 | \([0, 0, 0, -452748, -81209072]\) | \(53706380371489/16171875000\) | \(3090493440000000000\) | \([2]\) | \(737280\) | \(2.2531\) |
Rank
sage: E.rank()
The elliptic curves in class 66240eu have rank \(0\).
Complex multiplication
The elliptic curves in class 66240eu do not have complex multiplication.Modular form 66240.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
