Properties

Label 23184bh
Number of curves $2$
Conductor $23184$
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 23184bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23184.ba2 23184bh1 \([0, 0, 0, 4965, 633418]\) \(4533086375/60669952\) \(-181159505952768\) \([2]\) \(64512\) \(1.4166\) \(\Gamma_0(N)\)-optimal
23184.ba1 23184bh2 \([0, 0, 0, -87195, 9278026]\) \(24553362849625/1755162752\) \(5240887894867968\) \([2]\) \(129024\) \(1.7632\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23184bh have rank \(1\).

Complex multiplication

The elliptic curves in class 23184bh do not have complex multiplication.

Modular form 23184.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{7} + 4q^{11} - 6q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.