Properties

Label 69300bj
Number of curves $4$
Conductor $69300$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 69300bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69300.z3 69300bj1 \([0, 0, 0, -598800, -180991375]\) \(-130287139815424/2250652635\) \(-410181442728750000\) \([2]\) \(995328\) \(2.1776\) \(\Gamma_0(N)\)-optimal
69300.z2 69300bj2 \([0, 0, 0, -9620175, -11484774250]\) \(33766427105425744/9823275\) \(28644669900000000\) \([2]\) \(1990656\) \(2.5241\)  
69300.z4 69300bj3 \([0, 0, 0, 2317200, -867344875]\) \(7549996227362816/6152409907875\) \(-1121276705710218750000\) \([2]\) \(2985984\) \(2.7269\)  
69300.z1 69300bj4 \([0, 0, 0, -11159175, -7565103250]\) \(52702650535889104/22020583921875\) \(64212022716187500000000\) \([2]\) \(5971968\) \(3.0734\)  

Rank

sage: E.rank()
 

The elliptic curves in class 69300bj have rank \(0\).

Complex multiplication

The elliptic curves in class 69300bj do not have complex multiplication.

Modular form 69300.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{7} + q^{11} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.