Properties

Label 4032.b
Number of curves 22
Conductor 40324032
CM no
Rank 00
Graph

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

Elliptic curves in class 4032.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.b1 4032k1 [0,0,0,3387,59740][0, 0, 0, -3387, 59740] 92100460096/2025380792100460096/20253807 944961619392944961619392 [2][2] 76807680 1.01141.0114 Γ0(N)\Gamma_0(N)-optimal
4032.b2 4032k2 [0,0,0,7548,365920][0, 0, 0, 7548, 365920] 15926924096/2858870715926924096/28588707 85365421682688-85365421682688 [2][2] 1536015360 1.35801.3580  

Rank

sage: E.rank()
 

The elliptic curves in class 4032.b have rank 00.

Complex multiplication

The elliptic curves in class 4032.b do not have complex multiplication.

Modular form 4032.2.a.b

sage: E.q_eigenform(10)
 
q4q5q7+2q11+2q134q19+O(q20)q - 4 q^{5} - q^{7} + 2 q^{11} + 2 q^{13} - 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 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.