Properties

Label 23400bm
Number of curves $2$
Conductor $23400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 23400bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23400.bb1 23400bm1 \([0, 0, 0, -146550, -20286875]\) \(1909913257984/129730653\) \(23643411509250000\) \([2]\) \(153600\) \(1.8904\) \(\Gamma_0(N)\)-optimal
23400.bb2 23400bm2 \([0, 0, 0, 126825, -87263750]\) \(77366117936/1172914587\) \(-3420218935692000000\) \([2]\) \(307200\) \(2.2370\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23400bm have rank \(0\).

Complex multiplication

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

Modular form 23400.2.a.bm

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} + q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) Copy content 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.