Properties

Label 67032.v
Number of curves $4$
Conductor $67032$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 67032.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67032.v1 67032ch4 \([0, 0, 0, -261435531, 1627027786006]\) \(22501000029889239268/3620708343\) \(317986928487882243072\) \([2]\) \(9437184\) \(3.3364\)  
67032.v2 67032ch2 \([0, 0, 0, -16389471, 25259710210]\) \(22174957026242512/278654127129\) \(6118165397630770331904\) \([2, 2]\) \(4718592\) \(2.9898\)  
67032.v3 67032ch3 \([0, 0, 0, -2815491, 65832336430]\) \(-28104147578308/21301741002339\) \(-1870814921028882387987456\) \([2]\) \(9437184\) \(3.3364\)  
67032.v4 67032ch1 \([0, 0, 0, -1922466, -401863259]\) \(572616640141312/280535480757\) \(384967039798368537552\) \([2]\) \(2359296\) \(2.6433\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 67032.v have rank \(0\).

Complex multiplication

The elliptic curves in class 67032.v do not have complex multiplication.

Modular form 67032.2.a.v

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