Properties

Label 83790ba
Number of curves $2$
Conductor $83790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 83790ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.i2 83790ba1 \([1, -1, 0, -44010360, 202017361216]\) \(-37702212117675062365927/48682087219200000000\) \(-12172809862899302400000000\) \([2]\) \(19169280\) \(3.5065\) \(\Gamma_0(N)\)-optimal
83790.i1 83790ba2 \([1, -1, 0, -850410360, 9541258321216]\) \(272011766516966956291165927/141259766579735040000\) \(35321580853963007546880000\) \([2]\) \(38338560\) \(3.8531\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83790ba have rank \(1\).

Complex multiplication

The elliptic curves in class 83790ba do not have complex multiplication.

Modular form 83790.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{11} + 2 q^{13} + q^{16} - 6 q^{17} - q^{19} + O(q^{20})\) 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.