Properties

Label 24336.r
Number of curves $2$
Conductor $24336$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 24336.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24336.r1 24336v2 \([0, 0, 0, -402051, -97278766]\) \(907924/9\) \(71245947275523072\) \([2]\) \(239616\) \(2.0526\)  
24336.r2 24336v1 \([0, 0, 0, -6591, -3712930]\) \(-16/3\) \(-5937162272960256\) \([2]\) \(119808\) \(1.7060\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24336.r have rank \(1\).

Complex multiplication

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

Modular form 24336.2.a.r

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