Properties

Label 294c
Number of curves $6$
Conductor $294$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("294.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 294c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
294.g5 294c1 [1, 0, 0, -197, -2367] [4] 192 \(\Gamma_0(N)\)-optimal
294.g4 294c2 [1, 0, 0, -4117, -101935] [2, 2] 384  
294.g1 294c3 [1, 0, 0, -65857, -6510547] [2] 768  
294.g3 294c4 [1, 0, 0, -5097, -49995] [2, 2] 768  
294.g2 294c5 [1, 0, 0, -44787, 3609423] [2] 1536  
294.g6 294c6 [1, 0, 0, 18913, -381333] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 294c have rank \(0\).

Modular form 294.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} + 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.