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Properties

Label 35322l
Number of curves $2$
Conductor $35322$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 35322l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35322.b2 35322l1 \([1, 1, 0, 412073, -187253675]\) \(533411731/1354752\) \(-19653585025100479488\) \([2]\) \(1559040\) \(2.3858\) \(\Gamma_0(N)\)-optimal
35322.b1 35322l2 \([1, 1, 0, -3490167, -2103253515]\) \(324101132909/56010528\) \(812552905881497948832\) \([2]\) \(3118080\) \(2.7324\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35322l have rank \(1\).

Complex multiplication

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

Modular form 35322.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 4 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 4 q^{10} + 4 q^{11} - q^{12} - 2 q^{13} - q^{14} + 4 q^{15} + q^{16} + 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.