Properties

Label 229320.bm
Number of curves $2$
Conductor $229320$
CM no
Rank $0$
Graph

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

Elliptic curves in class 229320.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.bm1 229320bt2 \([0, 0, 0, -10503003, -9590309498]\) \(4253577358972/1142578125\) \(34418802018510000000000\) \([2]\) \(17203200\) \(3.0326\)  
229320.bm2 229320bt1 \([0, 0, 0, -9700383, -11627519582]\) \(13404187799728/1584375\) \(11931851366416800000\) \([2]\) \(8601600\) \(2.6860\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.bm do not have complex multiplication.

Modular form 229320.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})\)  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 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.