Properties

Label 19110p
Number of curves 44
Conductor 1911019110
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 19110p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.e3 19110p1 [1,1,0,6805617032,216099982943424][1, 1, 0, -6805617032, -216099982943424] 296304326013275547793071733369/268420373544960000000296304326013275547793071733369/268420373544960000000 3157938852719099904000000031579388527190999040000000 [2][2] 2064384020643840 4.19114.1911 Γ0(N)\Gamma_0(N)-optimal
19110.e2 19110p2 [1,1,0,6854789512,212818772194496][1, 1, 0, -6854789512, -212818772194496] 302773487204995438715379645049/8911747415025000000000000302773487204995438715379645049/8911747415025000000000000 10484581716302762250000000000001048458171630276225000000000000 [2,2][2, 2] 4128768041287680 4.53774.5377  
19110.e1 19110p3 [1,1,0,16216549192,494082084186496][1, 1, 0, -16216549192, 494082084186496] 4008766897254067912673785886329/14234805107116699218750000004008766897254067912673785886329/1423480510711669921875000000 167471058604717254638671875000000167471058604717254638671875000000 [4][4] 8257536082575360 4.88434.8843  
19110.e4 19110p4 [1,1,0,1720210488,709721157194496][1, 1, 0, 1720210488, -709721157194496] 4784981304203817469820354951/18523438364829100780350000004784981304203817469820354951/1852343836482910078035000000 217926400018377887770739715000000-217926400018377887770739715000000 [2][2] 8257536082575360 4.88434.8843  

Rank

sage: E.rank()
 

The elliptic curves in class 19110p have rank 00.

Complex multiplication

The elliptic curves in class 19110p do not have complex multiplication.

Modular form 19110.2.a.p

sage: E.q_eigenform(10)
 
qq2q3+q4+q5+q6q8+q9q104q11q12+q13q15+q16+2q17q188q19+O(q20)q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} + q^{13} - q^{15} + q^{16} + 2 q^{17} - q^{18} - 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.

(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 Cremona labels.