Properties

Label 15680.cd
Number of curves $2$
Conductor $15680$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15680.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.cd1 15680n1 \([0, 1, 0, -195281, -33300625]\) \(-177953104/125\) \(-578509309952000\) \([]\) \(96768\) \(1.7689\) \(\Gamma_0(N)\)-optimal
15680.cd2 15680n2 \([0, 1, 0, 188879, -141095921]\) \(161017136/1953125\) \(-9039207968000000000\) \([]\) \(290304\) \(2.3182\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15680.cd have rank \(0\).

Complex multiplication

The elliptic curves in class 15680.cd do not have complex multiplication.

Modular form 15680.2.a.cd

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2q^{9} - 6q^{11} + 2q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.