Properties

Label 55545.u
Number of curves $2$
Conductor $55545$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 55545.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55545.u1 55545l1 \([1, 0, 1, -760449, 254433247]\) \(328523283207001/1109390625\) \(164229627420140625\) \([2]\) \(608256\) \(2.1674\) \(\Gamma_0(N)\)-optimal
55545.u2 55545l2 \([1, 0, 1, -429824, 477142247]\) \(-59323563117001/630142750125\) \(-93283742211659236125\) \([2]\) \(1216512\) \(2.5140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55545.u have rank \(0\).

Complex multiplication

The elliptic curves in class 55545.u do not have complex multiplication.

Modular form 55545.2.a.u

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