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Properties

Label 702.a
Number of curves $3$
Conductor $702$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 702.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
702.a1 702e3 \([1, -1, 0, -472266, 125037036]\) \(-47937788722586831331/1352\) \(-328536\) \([3]\) \(3240\) \(1.4950\)  
702.a2 702e1 \([1, -1, 0, -5826, 173076]\) \(-810052784622459/2471326208\) \(-66725807616\) \([3]\) \(1080\) \(0.94568\) \(\Gamma_0(N)\)-optimal
702.a3 702e2 \([1, -1, 0, 11919, 881693]\) \(9513304174269/22682796032\) \(-446465474297856\) \([]\) \(3240\) \(1.4950\)  

Rank

sage: E.rank()
 

The elliptic curves in class 702.a have rank \(0\).

Complex multiplication

The elliptic curves in class 702.a do not have complex multiplication.

Modular form 702.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 3 q^{5} - q^{7} - q^{8} + 3 q^{10} - 3 q^{11} + q^{13} + q^{14} + q^{16} + 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.