Properties

Label 92736.cv
Number of curves $2$
Conductor $92736$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92736.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.cv1 92736bb2 \([0, 0, 0, -17580, -897104]\) \(12576878500/1127\) \(53843263488\) \([2]\) \(122880\) \(1.0991\)  
92736.cv2 92736bb1 \([0, 0, 0, -1020, -16112]\) \(-9826000/3703\) \(-44228395008\) \([2]\) \(61440\) \(0.75255\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 92736.cv have rank \(0\).

Complex multiplication

The elliptic curves in class 92736.cv do not have complex multiplication.

Modular form 92736.2.a.cv

sage: E.q_eigenform(10)
 
\(q - q^{7} + 4q^{11} - 6q^{13} + O(q^{20})\)  Toggle raw display

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.