Properties

Label 243360bj
Number of curves $4$
Conductor $243360$
CM no
Rank $1$
Graph

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

Elliptic curves in class 243360bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.bj3 243360bj1 \([0, 0, 0, -100893, 11503492]\) \(504358336/38025\) \(8563214816769600\) \([2, 2]\) \(1032192\) \(1.8024\) \(\Gamma_0(N)\)-optimal
243360.bj1 243360bj2 \([0, 0, 0, -1583868, 767227552]\) \(30488290624/195\) \(2810491016785920\) \([2]\) \(2064384\) \(2.1490\)  
243360.bj4 243360bj3 \([0, 0, 0, 96837, 51089038]\) \(55742968/658125\) \(-1185675897706560000\) \([2]\) \(2064384\) \(2.1490\)  
243360.bj2 243360bj4 \([0, 0, 0, -329043, -59086118]\) \(2186875592/428415\) \(771831095484833280\) \([2]\) \(2064384\) \(2.1490\)  

Rank

sage: E.rank()
 

The elliptic curves in class 243360bj have rank \(1\).

Complex multiplication

The elliptic curves in class 243360bj do not have complex multiplication.

Modular form 243360.2.a.bj

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.