Properties

Label 8624.k
Number of curves $2$
Conductor $8624$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8624.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8624.k1 8624m2 \([0, -1, 0, -4328, 109936]\) \(911871625/10648\) \(104717713408\) \([]\) \(6912\) \(0.92682\)  
8624.k2 8624m1 \([0, -1, 0, -408, -2960]\) \(765625/22\) \(216358912\) \([]\) \(2304\) \(0.37751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8624.k have rank \(1\).

Complex multiplication

The elliptic curves in class 8624.k do not have complex multiplication.

Modular form 8624.2.a.k

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