Properties

Label 38640cv
Number of curves $2$
Conductor $38640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 38640cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.cv1 38640cv1 \([0, 1, 0, -3920, -91500]\) \(1626794704081/83462400\) \(341861990400\) \([2]\) \(73728\) \(0.97102\) \(\Gamma_0(N)\)-optimal
38640.cv2 38640cv2 \([0, 1, 0, 2480, -355180]\) \(411664745519/13605414480\) \(-55727777710080\) \([2]\) \(147456\) \(1.3176\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38640cv have rank \(0\).

Complex multiplication

The elliptic curves in class 38640cv do not have complex multiplication.

Modular form 38640.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 6q^{11} + q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.