Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("96192.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 96192.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96192.u1 96192f2 [0, 0, 0, -71724, 7373360] [2] 442368  
96192.u2 96192f1 [0, 0, 0, -2604, 212528] [2] 221184 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 96192.2.a.u

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.