Properties

Label 67600b
Number of curves 4
Conductor 67600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("67600.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67600b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67600.cb3 67600b1 [0, 0, 0, -8450, -274625] [2] 110592 \(\Gamma_0(N)\)-optimal
67600.cb2 67600b2 [0, 0, 0, -29575, 1647750] [2, 2] 221184  
67600.cb4 67600b3 [0, 0, 0, 54925, 9337250] [2] 442368  
67600.cb1 67600b4 [0, 0, 0, -452075, 116990250] [2] 442368  

Rank

sage: E.rank()
 

The elliptic curves in class 67600b have rank \(1\).

Modular form 67600.2.a.cb

sage: E.q_eigenform(10)
 
\( q + 4q^{7} - 3q^{9} + 4q^{11} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.