Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 83790.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.u1 83790j2 \([1, -1, 0, -343695, 74974325]\) \(1413487789441083/55278125000\) \(175592235459375000\) \([2]\) \(1179648\) \(2.0761\)  
83790.u2 83790j1 \([1, -1, 0, -55575, -3451939]\) \(5976054062523/1824760000\) \(5796392109480000\) \([2]\) \(589824\) \(1.7295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 83790.2.a.u

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