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Properties

Label 83790dd
Number of curves $2$
Conductor $83790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dd1")
 
E.isogeny_class()
 

Elliptic curves in class 83790dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.fm2 83790dd1 \([1, -1, 1, 35638, 1780489]\) \(2161700757/1848320\) \(-4280127392701440\) \([2]\) \(691200\) \(1.6870\) \(\Gamma_0(N)\)-optimal
83790.fm1 83790dd2 \([1, -1, 1, -176042, 15836041]\) \(260549802603/104256800\) \(241425935744565600\) \([2]\) \(1382400\) \(2.0336\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83790dd have rank \(0\).

Complex multiplication

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

Modular form 83790.2.a.dd

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