Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 105222.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 105222.j1 | 105222i2 | \([1, 1, 1, -180635687, 899709589469]\) | \(651830049594992807318443118833/27463741155896711966097408\) | \(27463741155896711966097408\) | \([2]\) | \(42024960\) | \(3.6459\) | |
| 105222.j2 | 105222i1 | \([1, 1, 1, 5486553, 52257806301]\) | \(18265116376750268914741007/1190206309258976028524544\) | \(-1190206309258976028524544\) | \([2]\) | \(21012480\) | \(3.2993\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 105222.j have rank \(0\).
Complex multiplication
The elliptic curves in class 105222.j do not have complex multiplication.Modular form 105222.2.a.j
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.
