↑

Properties

Label 440818m
Number of curves $2$
Conductor $440818$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 440818m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.m2 440818m1 \([1, 1, 0, -5504, 142220]\) \(7189057/644\) \(1652327807396\) \([2]\) \(1192320\) \(1.0842\) \(\Gamma_0(N)\)-optimal
440818.m1 440818m2 \([1, 1, 0, -19194, -868102]\) \(304821217/51842\) \(133012388495378\) \([2]\) \(2384640\) \(1.4308\)  

Rank

sage: E.rank()
 

The elliptic curves in class 440818m have rank \(0\).

Complex multiplication

The elliptic curves in class 440818m do not have complex multiplication.

Modular form 440818.2.a.m

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