↑

Properties

Label 53130.j
Number of curves $2$
Conductor $53130$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 53130.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53130.j1 53130j1 \([1, 1, 0, -629988348, -6086317362048]\) \(27651663563526365415678286540489/812537626226828906250000\) \(812537626226828906250000\) \([2]\) \(25344000\) \(3.6876\) \(\Gamma_0(N)\)-optimal
53130.j2 53130j2 \([1, 1, 0, -604105568, -6609247872612]\) \(-24381601518390837785713085858569/4759531575193405151367187500\) \(-4759531575193405151367187500\) \([2]\) \(50688000\) \(4.0341\)  

Rank

sage: E.rank()
 

The elliptic curves in class 53130.j have rank \(0\).

Complex multiplication

The elliptic curves in class 53130.j do not have complex multiplication.

Modular form 53130.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.