Properties

Label 7623p
Number of curves 66
Conductor 76237623
CM no
Rank 00
Graph

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

Elliptic curves in class 7623p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7623.g6 7623p1 [1,1,1,1066,3220][1, -1, 1, 1066, -3220] 103823/63103823/63 81362482047-81362482047 [2][2] 51205120 0.782740.78274 Γ0(N)\Gamma_0(N)-optimal
7623.g5 7623p2 [1,1,1,4379,22822][1, -1, 1, -4379, -22822] 7189057/39697189057/3969 51258363689615125836368961 [2,2][2, 2] 1024010240 1.12931.1293  
7623.g2 7623p3 [1,1,1,53384,4727302][1, -1, 1, -53384, -4727302] 13027640977/2160913027640977/21609 2790733134212127907331342121 [2,2][2, 2] 2048020480 1.47591.4759  
7623.g3 7623p4 [1,1,1,42494,3361790][1, -1, 1, -42494, 3361790] 6570725617/459276570725617/45927 5931324941226359313249412263 [2][2] 2048020480 1.47591.4759  
7623.g1 7623p5 [1,1,1,853799,303442180][1, -1, 1, -853799, -303442180] 53297461115137/14753297461115137/147 189845791443189845791443 [2][2] 4096040960 1.82251.8225  
7623.g4 7623p6 [1,1,1,37049,7687204][1, -1, 1, -37049, -7687204] 4354703137/17294403-4354703137/17294403 22335167517477507-22335167517477507 [2][2] 4096040960 1.82251.8225  

Rank

sage: E.rank()
 

The elliptic curves in class 7623p have rank 00.

Complex multiplication

The elliptic curves in class 7623p do not have complex multiplication.

Modular form 7623.2.a.p

sage: E.q_eigenform(10)
 
qq2q4+2q5+q7+3q82q10+2q13q14q166q174q19+O(q20)q - q^{2} - q^{4} + 2 q^{5} + q^{7} + 3 q^{8} - 2 q^{10} + 2 q^{13} - q^{14} - q^{16} - 6 q^{17} - 4 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.

(124488212244421422424188842814842841)\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.