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Properties

Label 35322q
Number of curves $2$
Conductor $35322$
CM no
Rank $0$
Graph

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

Elliptic curves in class 35322q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35322.s2 35322q1 \([1, 0, 1, -370899, 97889374]\) \(-9486391169809/1473906672\) \(-876714061483097712\) \([2]\) \(725760\) \(2.1717\) \(\Gamma_0(N)\)-optimal
35322.s1 35322q2 \([1, 0, 1, -6140159, 5855610854]\) \(43040219271568849/841158108\) \(500340459286636668\) \([2]\) \(1451520\) \(2.5182\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35322q have rank \(0\).

Complex multiplication

The elliptic curves in class 35322q do not have complex multiplication.

Modular form 35322.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 4 q^{10} + q^{12} + 2 q^{13} + q^{14} + 4 q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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 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.