Properties

Label 912.k
Number of curves 44
Conductor 912912
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 912.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.k1 912k3 [0,1,0,1400832,637689780][0, 1, 0, -1400832, 637689780] 74220219816682217473/1641674220219816682217473/16416 6723993667239936 [2][2] 57605760 1.79461.7946  
912.k2 912k2 [0,1,0,87552,9941940][0, 1, 0, -87552, 9941940] 18120364883707393/26948505618120364883707393/269485056 11038107893761103810789376 [2,2][2, 2] 28802880 1.44801.4480  
912.k3 912k4 [0,1,0,84992,10553268][0, 1, 0, -84992, 10553268] 16576888679672833/2216253521952-16576888679672833/2216253521952 9077774425915392-9077774425915392 [4][4] 57605760 1.79461.7946  
912.k4 912k1 [0,1,0,5632,144308][0, 1, 0, -5632, 144308] 4824238966273/5379194884824238966273/537919488 22033182228482203318222848 [2][2] 14401440 1.10141.1014 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 912.k have rank 00.

Complex multiplication

The elliptic curves in class 912.k do not have complex multiplication.

Modular form 912.2.a.k

sage: E.q_eigenform(10)
 
q+q3+2q5+q9+4q11+2q13+2q156q17+q19+O(q20)q + q^{3} + 2 q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} - 6 q^{17} + q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1244212242144241)\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 LMFDB labels.