Properties

Label 29760cm
Number of curves $6$
Conductor $29760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("29760.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29760cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29760.bu6 29760cm1 [0, 1, 0, 3839, 519935] [2] 98304 \(\Gamma_0(N)\)-optimal
29760.bu5 29760cm2 [0, 1, 0, -78081, 7909119] [2, 2] 196608  
29760.bu4 29760cm3 [0, 1, 0, -236801, -34659585] [2] 393216  
29760.bu2 29760cm4 [0, 1, 0, -1230081, 524696319] [2, 2] 393216  
29760.bu3 29760cm5 [0, 1, 0, -1210881, 541887999] [2] 786432  
29760.bu1 29760cm6 [0, 1, 0, -19681281, 33600317439] [2] 786432  

Rank

sage: E.rank()
 

The elliptic curves in class 29760cm have rank \(0\).

Modular form 29760.2.a.bu

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

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.