Properties

Label 7744.k
Number of curves $3$
Conductor $7744$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7744.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7744.k1 7744y3 \([0, -1, 0, -3785041, -2833092073]\) \(-52893159101157376/11\) \(-1247178944\) \([]\) \(48000\) \(2.0422\)  
7744.k2 7744y2 \([0, -1, 0, -5001, -244913]\) \(-122023936/161051\) \(-18259946919104\) \([]\) \(9600\) \(1.2375\)  
7744.k3 7744y1 \([0, -1, 0, -161, 1927]\) \(-4096/11\) \(-1247178944\) \([]\) \(1920\) \(0.43279\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7744.k have rank \(1\).

Complex multiplication

The elliptic curves in class 7744.k do not have complex multiplication.

Modular form 7744.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} - 2 q^{9} + 4 q^{13} + q^{15} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.