Show commands:
SageMath
E = EllipticCurve("ko1")
E.isogeny_class()
Elliptic curves in class 346560.ko
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.ko1 | 346560ko2 | \([0, 1, 0, -233345, -43463457]\) | \(781484460931/900\) | \(1618241126400\) | \([2]\) | \(1474560\) | \(1.6267\) | |
346560.ko2 | 346560ko1 | \([0, 1, 0, -14465, -694305]\) | \(-186169411/6480\) | \(-11651336110080\) | \([2]\) | \(737280\) | \(1.2801\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.ko have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.ko do not have complex multiplication.Modular form 346560.2.a.ko
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.