Properties

Label 96192.x
Number of curves 2
Conductor 96192
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("96192.x1")
sage: E.isogeny_class()

Elliptic curves in class 96192.x

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
96192.x1 96192y2 [0, 0, 0, -71724, -7373360] 2 442368  
96192.x2 96192y1 [0, 0, 0, -2604, -212528] 2 221184 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 96192.x have rank \(0\).

Modular form None

sage: E.q_eigenform(10)
\( q + 2q^{5} + 4q^{7} + 4q^{11} + 4q^{17} - 4q^{19} + O(q^{20}) \)

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.