Properties

Label 92778.r
Number of curves $6$
Conductor $92778$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("92778.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92778.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92778.r1 92778m4 [1, 1, 1, -2968942, -1970259601] [2] 1695744  
92778.r2 92778m6 [1, 1, 1, -2019072, 1092828159] [2] 3391488  
92778.r3 92778m3 [1, 1, 1, -229782, -15100209] [2, 2] 1695744  
92778.r4 92778m2 [1, 1, 1, -185602, -30828289] [2, 2] 847872  
92778.r5 92778m1 [1, 1, 1, -8882, -715201] [2] 423936 \(\Gamma_0(N)\)-optimal
92778.r6 92778m5 [1, 1, 1, 852628, -115547857] [2] 3391488  

Rank

sage: E.rank()
 

The elliptic curves in class 92778.r have rank \(1\).

Modular form 92778.2.a.r

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 6q^{13} - q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.