Properties

Label 215600.bj
Number of curves $2$
Conductor $215600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 215600.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215600.bj1 215600be1 \([0, 1, 0, -37158, -2802437]\) \(-3937024/55\) \(-79266013750000\) \([]\) \(870912\) \(1.4730\) \(\Gamma_0(N)\)-optimal
215600.bj2 215600be2 \([0, 1, 0, 134342, -13949937]\) \(186050816/166375\) \(-239779691593750000\) \([]\) \(2612736\) \(2.0223\)  

Rank

sage: E.rank()
 

The elliptic curves in class 215600.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 215600.bj do not have complex multiplication.

Modular form 215600.2.a.bj

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{9} + q^{11} - 5 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.