Properties

Label 35739h
Number of curves $2$
Conductor $35739$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 35739h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35739.r1 35739h1 \([1, -1, 0, -1122, -12817]\) \(1157625/121\) \(16335689337\) \([2]\) \(25920\) \(0.69471\) \(\Gamma_0(N)\)-optimal
35739.r2 35739h2 \([1, -1, 0, 1443, -64630]\) \(2460375/14641\) \(-1976618409777\) \([2]\) \(51840\) \(1.0413\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35739h have rank \(0\).

Complex multiplication

The elliptic curves in class 35739h do not have complex multiplication.

Modular form 35739.2.a.h

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