Properties

Label 29760b
Number of curves $6$
Conductor $29760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("29760.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29760b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29760.n6 29760b1 [0, -1, 0, 3839, -519935] [2] 98304 \(\Gamma_0(N)\)-optimal
29760.n5 29760b2 [0, -1, 0, -78081, -7909119] [2, 2] 196608  
29760.n4 29760b3 [0, -1, 0, -236801, 34659585] [2] 393216  
29760.n2 29760b4 [0, -1, 0, -1230081, -524696319] [2, 2] 393216  
29760.n3 29760b5 [0, -1, 0, -1210881, -541887999] [2] 786432  
29760.n1 29760b6 [0, -1, 0, -19681281, -33600317439] [2] 786432  

Rank

sage: E.rank()
 

The elliptic curves in class 29760b have rank \(1\).

Modular form 29760.2.a.n

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.