Properties

Label 193200.dv
Number of curves $4$
Conductor $193200$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("dv1")
 
E.isogeny_class()
 

Elliptic curves in class 193200.dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
193200.dv1 193200bz3 \([0, 1, 0, -71539608, 232875328788]\) \(632678989847546725777/80515134\) \(5152968576000000\) \([2]\) \(11796480\) \(2.8749\)  
193200.dv2 193200bz4 \([0, 1, 0, -5115608, 2520208788]\) \(231331938231569617/90942310746882\) \(5820307887800448000000\) \([2]\) \(11796480\) \(2.8749\)  
193200.dv3 193200bz2 \([0, 1, 0, -4471608, 3636904788]\) \(154502321244119857/55101928644\) \(3526523433216000000\) \([2, 2]\) \(5898240\) \(2.5283\)  
193200.dv4 193200bz1 \([0, 1, 0, -239608, 73560788]\) \(-23771111713777/22848457968\) \(-1462301309952000000\) \([2]\) \(2949120\) \(2.1817\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 193200.dv have rank \(2\).

Complex multiplication

The elliptic curves in class 193200.dv do not have complex multiplication.

Modular form 193200.2.a.dv

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - 4 q^{11} - 2 q^{13} - 6 q^{17} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.