Properties

Label 65520.cv
Number of curves $8$
Conductor $65520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 65520.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65520.cv1 65520du7 \([0, 0, 0, -326257707, -2267864675494]\) \(1286229821345376481036009/247265484375000000\) \(738330780096000000000000\) \([2]\) \(15925248\) \(3.5804\)  
65520.cv2 65520du8 \([0, 0, 0, -143504427, 640907473754]\) \(109454124781830273937129/3914078300576808000\) \(11687375180269539459072000\) \([4]\) \(15925248\) \(3.5804\)  
65520.cv3 65520du5 \([0, 0, 0, -142249467, 653016395306]\) \(106607603143751752938169/5290068420\) \(15796059661025280\) \([4]\) \(5308416\) \(3.0311\)  
65520.cv4 65520du6 \([0, 0, 0, -22544427, -27493294246]\) \(424378956393532177129/136231857216000000\) \(406786145937260544000000\) \([2, 2]\) \(7962624\) \(3.2338\)  
65520.cv5 65520du4 \([0, 0, 0, -9901947, 7738316714]\) \(35958207000163259449/12145729518877500\) \(36266954011695912960000\) \([2]\) \(5308416\) \(3.0311\)  
65520.cv6 65520du2 \([0, 0, 0, -8891067, 10202235626]\) \(26031421522845051769/5797789779600\) \(17312107517249126400\) \([2, 2]\) \(2654208\) \(2.6845\)  
65520.cv7 65520du1 \([0, 0, 0, -492987, 196763114]\) \(-4437543642183289/3033210136320\) \(-9057116935689338880\) \([2]\) \(1327104\) \(2.3379\) \(\Gamma_0(N)\)-optimal
65520.cv8 65520du3 \([0, 0, 0, 3997653, -2931253414]\) \(2366200373628880151/2612420149248000\) \(-7800644766932140032000\) \([2]\) \(3981312\) \(2.8872\)  

Rank

sage: E.rank()
 

The elliptic curves in class 65520.cv have rank \(1\).

Complex multiplication

The elliptic curves in class 65520.cv do not have complex multiplication.

Modular form 65520.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.