Properties

Label 161700br
Number of curves $2$
Conductor $161700$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161700br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.dd2 161700br1 \([0, 1, 0, -100843633, 535048768988]\) \(-3856034557002072064/1973796785296875\) \(-58053804498348011718750000\) \([2]\) \(46448640\) \(3.6483\) \(\Gamma_0(N)\)-optimal
161700.dd1 161700br2 \([0, 1, 0, -1775265508, 28785894643988]\) \(1314817350433665559504/190690249278375\) \(89738068549406161500000000\) \([2]\) \(92897280\) \(3.9949\)  

Rank

sage: E.rank()
 

The elliptic curves in class 161700br have rank \(0\).

Complex multiplication

The elliptic curves in class 161700br do not have complex multiplication.

Modular form 161700.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - q^{11} - 2 q^{17} + 6 q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.