Properties

Label 35490.i
Number of curves $2$
Conductor $35490$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 35490.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.i1 35490h1 \([1, 1, 0, -38873, 693477]\) \(1345938541921/733824000\) \(3542028287616000\) \([2]\) \(322560\) \(1.6744\) \(\Gamma_0(N)\)-optimal
35490.i2 35490h2 \([1, 1, 0, 150407, 5652613]\) \(77958456780959/47911500000\) \(-231259659403500000\) \([2]\) \(645120\) \(2.0210\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35490.i have rank \(2\).

Complex multiplication

The elliptic curves in class 35490.i do not have complex multiplication.

Modular form 35490.2.a.i

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