Properties

Label 306.b
Number of curves 6
Conductor 306
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("306.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 306.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
306.b1 306c5 [1, -1, 0, -249696, 48087270] [2] 1024  
306.b2 306c3 [1, -1, 0, -15606, 754272] [2, 2] 512  
306.b3 306c6 [1, -1, 0, -14796, 835434] [2] 1024  
306.b4 306c2 [1, -1, 0, -1026, 10692] [2, 2] 256  
306.b5 306c1 [1, -1, 0, -306, -1836] [2] 128 \(\Gamma_0(N)\)-optimal
306.b6 306c4 [1, -1, 0, 2034, 60264] [2] 512  

Rank

sage: E.rank()
 

The elliptic curves in class 306.b have rank \(0\).

Modular form 306.2.a.b

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

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 LMFDB 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 LMFDB labels.