Properties

Label 5850.bj
Number of curves $2$
Conductor $5850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5850.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.bj1 5850cb2 \([1, -1, 1, -1445, 3957]\) \(3659383421/2056392\) \(187388721000\) \([2]\) \(6144\) \(0.85317\)  
5850.bj2 5850cb1 \([1, -1, 1, 355, 357]\) \(54439939/32448\) \(-2956824000\) \([2]\) \(3072\) \(0.50660\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 5850.bj do not have complex multiplication.

Modular form 5850.2.a.bj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2q^{7} + q^{8} - 2q^{11} + q^{13} - 2q^{14} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.