Properties

Label 3150k
Number of curves 88
Conductor 31503150
CM no
Rank 00
Graph

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

Elliptic curves in class 3150k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.f7 3150k1 [1,1,0,111942,14382284][1, -1, 0, -111942, -14382284] 13619385906841/604800013619385906841/6048000 6889050000000068890500000000 [2][2] 1843218432 1.61381.6138 Γ0(N)\Gamma_0(N)-optimal
3150.f6 3150k2 [1,1,0,129942,9432284][1, -1, 0, -129942, -9432284] 21302308926361/893025000021302308926361/8930250000 101721128906250000101721128906250000 [2,2][2, 2] 3686436864 1.96041.9604  
3150.f5 3150k3 [1,1,0,331317,55868341][1, -1, 0, -331317, 55868341] 353108405631241/86318776320353108405631241/86318776320 983224811520000000983224811520000000 [2][2] 5529655296 2.16312.1631  
3150.f4 3150k4 [1,1,0,980442,367339216][1, -1, 0, -980442, 367339216] 9150443179640281/1845703125009150443179640281/184570312500 21023712158203125002102371215820312500 [2][2] 7372873728 2.30702.3070  
3150.f8 3150k5 [1,1,0,432558,69619784][1, -1, 0, 432558, -69619784] 785793873833639/637994920500785793873833639/637994920500 7267160891320312500-7267160891320312500 [2][2] 7372873728 2.30702.3070  
3150.f2 3150k6 [1,1,0,4939317,4226108341][1, -1, 0, -4939317, 4226108341] 1169975873419524361/1084253184001169975873419524361/108425318400 12350321424000000001235032142400000000 [2,2][2, 2] 110592110592 2.50972.5097  
3150.f1 3150k7 [1,1,0,79027317,270424292341][1, -1, 0, -79027317, 270424292341] 4791901410190533590281/411600004791901410190533590281/41160000 468838125000000468838125000000 [2][2] 221184221184 2.85632.8563  
3150.f3 3150k8 [1,1,0,4579317,4867988341][1, -1, 0, -4579317, 4867988341] 932348627918877961/358766164249920-932348627918877961/358766164249920 4086570839659245000000-4086570839659245000000 [2][2] 221184221184 2.85632.8563  

Rank

sage: E.rank()
 

The elliptic curves in class 3150k have rank 00.

Complex multiplication

The elliptic curves in class 3150k do not have complex multiplication.

Modular form 3150.2.a.k

sage: E.q_eigenform(10)
 
qq2+q4q7q82q13+q14+q166q17+8q19+O(q20)q - q^{2} + q^{4} - q^{7} - q^{8} - 2 q^{13} + q^{14} + q^{16} - 6 q^{17} + 8 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 Cremona numbering.

(1234461212216223663611212244421214631242124161236326612212643122141264123241)\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.