Properties

Label 127050.bm
Number of curves $2$
Conductor $127050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 127050.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.bm1 127050v2 \([1, 1, 0, -1060325, 444202125]\) \(-7620530425/526848\) \(-9114681345000000000\) \([]\) \(3499200\) \(2.3890\)  
127050.bm2 127050v1 \([1, 1, 0, 74050, 661500]\) \(2595575/1512\) \(-26158205390625000\) \([]\) \(1166400\) \(1.8397\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 127050.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 127050.bm do not have complex multiplication.

Modular form 127050.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - q^{12} - q^{13} - q^{14} + q^{16} + 3q^{17} - q^{18} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.