Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("di1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161700di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.bo2 161700di1 \([0, -1, 0, -26133, -5090238]\) \(-67108864/343035\) \(-10089431178750000\) \([2]\) \(1105920\) \(1.7552\) \(\Gamma_0(N)\)-optimal
161700.bo1 161700di2 \([0, -1, 0, -632508, -193066488]\) \(59466754384/121275\) \(57071529900000000\) \([2]\) \(2211840\) \(2.1017\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 161700.2.a.di

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{11} - 6q^{13} + 2q^{17} + O(q^{20})\)  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.