Properties

Label 5070.j
Number of curves $2$
Conductor $5070$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 5070.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.j1 5070i1 \([1, 0, 1, -849, 9466]\) \(-2365581049/6750\) \(-192786750\) \([3]\) \(3024\) \(0.46139\) \(\Gamma_0(N)\)-optimal
5070.j2 5070i2 \([1, 0, 1, 1686, 49012]\) \(18573478391/46875000\) \(-1338796875000\) \([]\) \(9072\) \(1.0107\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5070.j have rank \(0\).

Complex multiplication

The elliptic curves in class 5070.j do not have complex multiplication.

Modular form 5070.2.a.j

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.