Properties

Label 35574.q
Number of curves $4$
Conductor $35574$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 35574.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35574.q1 35574q3 \([1, 1, 0, -59675508, -177461094180]\) \(112763292123580561/1932612\) \(402799592828562468\) \([2]\) \(4320000\) \(2.9198\)  
35574.q2 35574q4 \([1, 1, 0, -59616218, -177831241650]\) \(-112427521449300721/466873642818\) \(-97306915836949221050802\) \([2]\) \(8640000\) \(3.2663\)  
35574.q3 35574q1 \([1, 1, 0, -266928, 38580480]\) \(10091699281/2737152\) \(570483734505366528\) \([2]\) \(864000\) \(2.1150\) \(\Gamma_0(N)\)-optimal
35574.q4 35574q2 \([1, 1, 0, 681712, 252024480]\) \(168105213359/228637728\) \(-47653219447901397792\) \([2]\) \(1728000\) \(2.4616\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35574.q have rank \(1\).

Complex multiplication

The elliptic curves in class 35574.q do not have complex multiplication.

Modular form 35574.2.a.q

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.