Properties

Label 23400bk
Number of curves $4$
Conductor $23400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23400bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23400.c4 23400bk1 \([0, 0, 0, -4575, -422750]\) \(-3631696/24375\) \(-71077500000000\) \([2]\) \(73728\) \(1.3413\) \(\Gamma_0(N)\)-optimal
23400.c3 23400bk2 \([0, 0, 0, -117075, -15385250]\) \(15214885924/38025\) \(443523600000000\) \([2, 2]\) \(147456\) \(1.6878\)  
23400.c2 23400bk3 \([0, 0, 0, -162075, -2470250]\) \(20183398562/11567205\) \(269839758240000000\) \([2]\) \(294912\) \(2.0344\)  
23400.c1 23400bk4 \([0, 0, 0, -1872075, -985900250]\) \(31103978031362/195\) \(4548960000000\) \([2]\) \(294912\) \(2.0344\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23400bk have rank \(1\).

Complex multiplication

The elliptic curves in class 23400bk do not have complex multiplication.

Modular form 23400.2.a.bk

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 4q^{11} - q^{13} + 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.