Properties

Label 7744m
Number of curves $2$
Conductor $7744$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7744m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7744.c2 7744m1 [0, 1, 0, -161, -3137] [] 3072 \(\Gamma_0(N)\)-optimal
7744.c1 7744m2 [0, 1, 0, -232481, 43068991] [] 33792  

Rank

sage: E.rank()
 

The elliptic curves in class 7744m have rank \(2\).

Complex multiplication

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

Modular form 7744.2.a.m

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} - 2q^{7} + q^{9} - q^{13} + 2q^{15} - 5q^{17} - 6q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.