Properties

Label 24336.a
Number of curves $2$
Conductor $24336$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 24336.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24336.a1 24336r2 \([0, 0, 0, -91767, 9732710]\) \(94875856/9477\) \(8536866463487232\) \([2]\) \(258048\) \(1.7933\)  
24336.a2 24336r1 \([0, 0, 0, 7098, 735995]\) \(702464/4563\) \(-256896444503088\) \([2]\) \(129024\) \(1.4467\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24336.a have rank \(0\).

Complex multiplication

The elliptic curves in class 24336.a do not have complex multiplication.

Modular form 24336.2.a.a

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - 4 q^{7} + 2 q^{11} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.