Properties

Label 1850.j
Number of curves $2$
Conductor $1850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 1850.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.j1 1850o2 \([1, -1, 1, -341430, -76703803]\) \(2253707317528029/700928\) \(1369000000000\) \([2]\) \(8640\) \(1.6910\)  
1850.j2 1850o1 \([1, -1, 1, -21430, -1183803]\) \(557238592989/9699328\) \(18944000000000\) \([2]\) \(4320\) \(1.3445\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1850.j have rank \(1\).

Complex multiplication

The elliptic curves in class 1850.j do not have complex multiplication.

Modular form 1850.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.