↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 35322.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35322.r1 35322s2 \([1, 0, 1, -116917, -15395008]\) \(249896037845497/37933056\) \(26829329780736\) \([]\) \(285120\) \(1.5893\)  
35322.r2 35322s1 \([1, 0, 1, -3382, 45752]\) \(6045996937/2204496\) \(1559198135376\) \([3]\) \(95040\) \(1.0400\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 35322.2.a.r

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.