Properties

Label 7600l
Number of curves 33
Conductor 76007600
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 7600l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.n2 7600l1 [0,1,0,6208,190412][0, 1, 0, -6208, -190412] 413493625/152-413493625/152 9728000000-9728000000 [][] 69126912 0.884420.88442 Γ0(N)\Gamma_0(N)-optimal
7600.n3 7600l2 [0,1,0,3792,714412][0, 1, 0, 3792, -714412] 94196375/351180894196375/3511808 224755712000000-224755712000000 [][] 2073620736 1.43371.4337  
7600.n1 7600l3 [0,1,0,34208,19577588][0, 1, 0, -34208, 19577588] 69173457625/2550136832-69173457625/2550136832 163208757248000000-163208757248000000 [][] 6220862208 1.98301.9830  

Rank

sage: E.rank()
 

The elliptic curves in class 7600l have rank 00.

Complex multiplication

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

Modular form 7600.2.a.l

sage: E.q_eigenform(10)
 
q+q3q72q9+6q115q133q17q19+O(q20)q + q^{3} - q^{7} - 2 q^{9} + 6 q^{11} - 5 q^{13} - 3 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 Cremona numbering.

(139313931)\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.