Properties

Label 784c
Number of curves $4$
Conductor $784$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 784c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
784.e4 784c1 [0, 0, 0, 49, 686] [2] 192 \(\Gamma_0(N)\)-optimal
784.e3 784c2 [0, 0, 0, -931, 10290] [2, 2] 384  
784.e2 784c3 [0, 0, 0, -2891, -47334] [2] 768  
784.e1 784c4 [0, 0, 0, -14651, 682570] [4] 768  

Rank

sage: E.rank()
 

The elliptic curves in class 784c have rank \(0\).

Complex multiplication

The elliptic curves in class 784c do not have complex multiplication.

Modular form 784.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.