↑

Properties

Label 70395g
Number of curves $8$
Conductor $70395$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 70395g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70395.n6 70395g1 \([1, 1, 0, -39717, -3063096]\) \(147281603041/5265\) \(247696563465\) \([2]\) \(165888\) \(1.2753\) \(\Gamma_0(N)\)-optimal
70395.n5 70395g2 \([1, 1, 0, -41522, -2771769]\) \(168288035761/27720225\) \(1304122406643225\) \([2, 2]\) \(331776\) \(1.6219\)  
70395.n7 70395g3 \([1, 1, 0, 75803, -15466334]\) \(1023887723039/2798036865\) \(-131636109384403065\) \([2]\) \(663552\) \(1.9685\)  
70395.n4 70395g4 \([1, 1, 0, -187727, 28603824]\) \(15551989015681/1445900625\) \(68023668741575625\) \([2, 2]\) \(663552\) \(1.9685\)  
70395.n8 70395g5 \([1, 1, 0, 218398, 135902049]\) \(24487529386319/183539412225\) \(-8634773346347295225\) \([2]\) \(1327104\) \(2.3151\)  
70395.n2 70395g6 \([1, 1, 0, -2933132, 1932267651]\) \(59319456301170001/594140625\) \(27951869141015625\) \([2, 2]\) \(1327104\) \(2.3151\)  
70395.n3 70395g7 \([1, 1, 0, -2862737, 2029511304]\) \(-55150149867714721/5950927734375\) \(-279966638031005859375\) \([2]\) \(2654208\) \(2.6616\)  
70395.n1 70395g8 \([1, 1, 0, -46930007, 123724417026]\) \(242970740812818720001/24375\) \(1146743349375\) \([2]\) \(2654208\) \(2.6616\)  

Rank

sage: E.rank()
 

The elliptic curves in class 70395g have rank \(1\).

Complex multiplication

The elliptic curves in class 70395g do not have complex multiplication.

Modular form 70395.2.a.g

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 8 & 8 \\ 8 & 4 & 8 & 2 & 4 & 1 & 2 & 2 \\ 16 & 8 & 16 & 4 & 8 & 2 & 1 & 4 \\ 16 & 8 & 16 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.