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Properties

Label 34790q
Number of curves $2$
Conductor $34790$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 34790q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34790.y2 34790q1 \([1, 0, 0, -54146, -4184860]\) \(149222774347921/22187500000\) \(2610337187500000\) \([]\) \(237600\) \(1.6827\) \(\Gamma_0(N)\)-optimal
34790.y1 34790q2 \([1, 0, 0, -8886396, 10195417490]\) \(659648323242974383921/90211467550\) \(10613288945789950\) \([]\) \(1188000\) \(2.4874\)  

Rank

sage: E.rank()
 

The elliptic curves in class 34790q have rank \(0\).

Complex multiplication

The elliptic curves in class 34790q do not have complex multiplication.

Modular form 34790.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} - 2 q^{9} - q^{10} + 2 q^{11} + q^{12} + q^{13} - q^{15} + q^{16} - 8 q^{17} - 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.