Properties

Label 470925bm
Number of curves $2$
Conductor $470925$
CM no
Rank $0$
Graph

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

Elliptic curves in class 470925bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
470925.bm1 470925bm1 \([0, 0, 1, -9829650, -11861925719]\) \(-9221261135586623488/121324931\) \(-1381966792171875\) \([]\) \(11197440\) \(2.4636\) \(\Gamma_0(N)\)-optimal*
470925.bm2 470925bm2 \([0, 0, 1, -9273900, -13262313344]\) \(-7743965038771437568/2189290237869371\) \(-24937384115730804046875\) \([]\) \(33592320\) \(3.0129\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 470925bm1.

Rank

sage: E.rank()
 

The elliptic curves in class 470925bm have rank \(0\).

Complex multiplication

The elliptic curves in class 470925bm do not have complex multiplication.

Modular form 470925.2.a.bm

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{7} - 3 q^{11} - q^{13} + 4 q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.