Properties

Label 23100.bh
Number of curves $2$
Conductor $23100$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23100.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23100.bh1 23100bc2 \([0, 1, 0, -12908, 559188]\) \(59466754384/121275\) \(485100000000\) \([2]\) \(46080\) \(1.1288\)  
23100.bh2 23100bc1 \([0, 1, 0, -533, 14688]\) \(-67108864/343035\) \(-85758750000\) \([2]\) \(23040\) \(0.78222\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 23100.bh have rank \(1\).

Complex multiplication

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

Modular form 23100.2.a.bh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.