Properties

Label 112632.b
Number of curves 22
Conductor 112632112632
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 112632.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
112632.b1 112632d1 [0,1,0,1140880,469004956][0, -1, 0, -1140880, 469004956] 497005996/507497005996/507 167529126680527872167529126680527872 [2][2] 40128004012800 2.22352.2235 Γ0(N)\Gamma_0(N)-optimal
112632.b2 112632d2 [0,1,0,866520,700016076][0, -1, 0, -866520, 700016076] 108879878/257049-108879878/257049 169874534454055262208-169874534454055262208 [2][2] 80256008025600 2.57012.5701  

Rank

sage: E.rank()
 

The elliptic curves in class 112632.b have rank 00.

Complex multiplication

The elliptic curves in class 112632.b do not have complex multiplication.

Modular form 112632.2.a.b

sage: E.q_eigenform(10)
 
qq34q5+q96q11+q13+4q156q17+O(q20)q - q^{3} - 4 q^{5} + q^{9} - 6 q^{11} + q^{13} + 4 q^{15} - 6 q^{17} + 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.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.