↑

Properties

Label 45570.w
Number of curves $2$
Conductor $45570$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 45570.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45570.w1 45570be2 \([1, 0, 1, -1834684, -892448518]\) \(5805223604235668521/435937500000000\) \(51287610937500000000\) \([2]\) \(1935360\) \(2.5273\)  
45570.w2 45570be1 \([1, 0, 1, 109636, -61835014]\) \(1238798620042199/14760960000000\) \(-1736612183040000000\) \([2]\) \(967680\) \(2.1808\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 45570.w have rank \(1\).

Complex multiplication

The elliptic curves in class 45570.w do not have complex multiplication.

Modular form 45570.2.a.w

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.