Properties

Label 188760bm
Number of curves $4$
Conductor $188760$
CM no
Rank $1$
Graph

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

Elliptic curves in class 188760bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.z4 188760bm1 \([0, -1, 0, -11934996, 17075441220]\) \(-414566786956390864/37694855859375\) \(-17095356554519100000000\) \([2]\) \(17694720\) \(3.0090\) \(\Gamma_0(N)\)-optimal
188760.z3 188760bm2 \([0, -1, 0, -194947496, 1047728636220]\) \(451669360369114547716/3285246875625\) \(5959695605994599040000\) \([2, 2]\) \(35389440\) \(3.3556\)  
188760.z1 188760bm3 \([0, -1, 0, -3119154496, 67051759357420]\) \(925014005732729613959858/48938175\) \(177555378669926400\) \([2]\) \(70778880\) \(3.7022\)  
188760.z2 188760bm4 \([0, -1, 0, -198940496, 1002574195020]\) \(239997788713612187858/19220920226046825\) \(69736514880667114176153600\) \([2]\) \(70778880\) \(3.7022\)  

Rank

sage: E.rank()
 

The elliptic curves in class 188760bm have rank \(1\).

Complex multiplication

The elliptic curves in class 188760bm do not have complex multiplication.

Modular form 188760.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4 q^{7} + q^{9} - q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.