Properties

Label 379050.bg
Number of curves $4$
Conductor $379050$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bg1 379050bg3 \([1, 1, 0, -113209667875, 14661283470602125]\) \(218289391029690300712901881/306514992000\) \(225316684974186750000000\) \([2]\) \(928972800\) \(4.6459\)  
379050.bg2 379050bg4 \([1, 1, 0, -7404899875, 206587166378125]\) \(61085713691774408830201/10268551781250000000\) \(7548329142859773925781250000000\) \([2]\) \(928972800\) \(4.6459\)  
379050.bg3 379050bg2 \([1, 1, 0, -7075667875, 229076016602125]\) \(53294746224000958661881/1997017344000000\) \(1467991255011876000000000000\) \([2, 2]\) \(464486400\) \(4.2993\)  
379050.bg4 379050bg1 \([1, 1, 0, -421715875, 3926242778125]\) \(-11283450590382195961/2530373271552000\) \(-1860056872172126208000000000\) \([2]\) \(232243200\) \(3.9527\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 379050.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 379050.bg do not have complex multiplication.

Modular form 379050.2.a.bg

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{16} - 6q^{17} - q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.