Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 246114o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
246114.o2 | 246114o1 | \([1, -1, 1, -1808852, 943274423]\) | \(-506814405937489/4048994304\) | \(-5229146450279448576\) | \([]\) | \(5644800\) | \(2.4197\) | \(\Gamma_0(N)\)-optimal |
246114.o1 | 246114o2 | \([1, -1, 1, -7754792, -92241497257]\) | \(-39934705050538129/2823126576537804\) | \(-3645977546031200783600076\) | \([]\) | \(39513600\) | \(3.3927\) |
Rank
sage: E.rank()
The elliptic curves in class 246114o have rank \(2\).
Complex multiplication
The elliptic curves in class 246114o do not have complex multiplication.Modular form 246114.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.