Properties

Label 7600.s
Number of curves 22
Conductor 76007600
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 7600.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.s1 7600d2 [0,1,0,508,1488][0, -1, 0, -508, -1488] 3631696/18053631696/1805 72200000007220000000 [2][2] 61446144 0.584640.58464  
7600.s2 7600d1 [0,1,0,117,238][0, -1, 0, 117, -238] 702464/475702464/475 118750000-118750000 [2][2] 30723072 0.238060.23806 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7600.s have rank 00.

Complex multiplication

The elliptic curves in class 7600.s do not have complex multiplication.

Modular form 7600.2.a.s

sage: E.q_eigenform(10)
 
q+2q3+4q7+q9+4q116q17+q19+O(q20)q + 2 q^{3} + 4 q^{7} + q^{9} + 4 q^{11} - 6 q^{17} + 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.