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Properties

Label 156702.r
Number of curves $2$
Conductor $156702$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 156702.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156702.r1 156702db1 \([1, 1, 0, -431, -26907]\) \(-181356420553/6192965376\) \(-303455303424\) \([]\) \(276480\) \(0.88350\) \(\Gamma_0(N)\)-optimal
156702.r2 156702db2 \([1, 1, 0, 3874, 712692]\) \(131169029575367/4533723856896\) \(-222152468987904\) \([]\) \(829440\) \(1.4328\)  

Rank

sage: E.rank()
 

The elliptic curves in class 156702.r have rank \(0\).

Complex multiplication

The elliptic curves in class 156702.r do not have complex multiplication.

Modular form 156702.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.