Properties

Label 67600.cb
Number of curves $4$
Conductor $67600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 67600.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67600.cb1 67600b4 \([0, 0, 0, -452075, 116990250]\) \(132304644/5\) \(386144720000000\) \([2]\) \(442368\) \(1.8850\)  
67600.cb2 67600b2 \([0, 0, 0, -29575, 1647750]\) \(148176/25\) \(482680900000000\) \([2, 2]\) \(221184\) \(1.5384\)  
67600.cb3 67600b1 \([0, 0, 0, -8450, -274625]\) \(55296/5\) \(6033511250000\) \([2]\) \(110592\) \(1.1918\) \(\Gamma_0(N)\)-optimal
67600.cb4 67600b3 \([0, 0, 0, 54925, 9337250]\) \(237276/625\) \(-48268090000000000\) \([2]\) \(442368\) \(1.8850\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 67600.cb do not have complex multiplication.

Modular form 67600.2.a.cb

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.