Properties

Label 23100b
Number of curves $4$
Conductor $23100$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23100b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23100.b3 23100b1 \([0, -1, 0, -66533, 6725562]\) \(-130287139815424/2250652635\) \(-562663158750000\) \([2]\) \(124416\) \(1.6283\) \(\Gamma_0(N)\)-optimal
23100.b2 23100b2 \([0, -1, 0, -1068908, 425718312]\) \(33766427105425744/9823275\) \(39293100000000\) \([2]\) \(248832\) \(1.9748\)  
23100.b4 23100b3 \([0, -1, 0, 257467, 32038062]\) \(7549996227362816/6152409907875\) \(-1538102476968750000\) \([2]\) \(373248\) \(2.1776\)  
23100.b1 23100b4 \([0, -1, 0, -1239908, 280602312]\) \(52702650535889104/22020583921875\) \(88082335687500000000\) \([2]\) \(746496\) \(2.5241\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23100b have rank \(0\).

Complex multiplication

The elliptic curves in class 23100b do not have complex multiplication.

Modular form 23100.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.