Properties

Label 73920ca
Number of curves $6$
Conductor $73920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 73920ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.eq4 73920ca1 \([0, 1, 0, -16961, 844575]\) \(2058561081361/12705\) \(3330539520\) \([2]\) \(131072\) \(1.0139\) \(\Gamma_0(N)\)-optimal
73920.eq3 73920ca2 \([0, 1, 0, -17281, 810719]\) \(2177286259681/161417025\) \(42314504601600\) \([2, 2]\) \(262144\) \(1.3604\)  
73920.eq5 73920ca3 \([0, 1, 0, 16319, 3612959]\) \(1833318007919/22507682505\) \(-5900253922590720\) \([2]\) \(524288\) \(1.7070\)  
73920.eq2 73920ca4 \([0, 1, 0, -56001, -4153185]\) \(74093292126001/14707625625\) \(3855515811840000\) \([2, 2]\) \(524288\) \(1.7070\)  
73920.eq6 73920ca5 \([0, 1, 0, 116479, -24540321]\) \(666688497209279/1381398046875\) \(-362125209600000000\) \([2]\) \(1048576\) \(2.0536\)  
73920.eq1 73920ca6 \([0, 1, 0, -848001, -300836385]\) \(257260669489908001/14267882475\) \(3740239783526400\) \([2]\) \(1048576\) \(2.0536\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73920ca have rank \(0\).

Complex multiplication

The elliptic curves in class 73920ca do not have complex multiplication.

Modular form 73920.2.a.ca

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.