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Properties

Label 73689v
Number of curves $2$
Conductor $73689$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 73689v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73689.x1 73689v1 \([1, 0, 1, -36, -35]\) \(3723875/1827\) \(2431737\) \([2]\) \(9984\) \(-0.081396\) \(\Gamma_0(N)\)-optimal
73689.x2 73689v2 \([1, 0, 1, 129, -233]\) \(180362125/123627\) \(-164547537\) \([2]\) \(19968\) \(0.26518\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73689v have rank \(0\).

Complex multiplication

The elliptic curves in class 73689v do not have complex multiplication.

Modular form 73689.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} + q^{7} - 3 q^{8} + q^{9} - q^{12} + 2 q^{13} + q^{14} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.