Properties

Label 174.c
Number of curves $4$
Conductor $174$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 174.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174.c1 174d3 \([1, 0, 1, -310, -2122]\) \(3279392280793/4698\) \(4698\) \([2]\) \(40\) \(-0.024261\)  
174.c2 174d4 \([1, 0, 1, -50, 86]\) \(13430356633/4243686\) \(4243686\) \([2]\) \(40\) \(-0.024261\)  
174.c3 174d2 \([1, 0, 1, -20, -34]\) \(822656953/30276\) \(30276\) \([2, 2]\) \(20\) \(-0.37083\)  
174.c4 174d1 \([1, 0, 1, 0, -2]\) \(12167/1392\) \(-1392\) \([2]\) \(10\) \(-0.71741\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 174.c have rank \(0\).

Complex multiplication

The elliptic curves in class 174.c do not have complex multiplication.

Modular form 174.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{8} + q^{9} - 2 q^{10} - 4 q^{11} + q^{12} + 6 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.