Properties

Label 125760.cc
Number of curves 22
Conductor 125760125760
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 125760.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
125760.cc1 125760bx1 [0,1,0,44865,3772737][0, 1, 0, -44865, -3772737] 38099255258449/1222387200-38099255258449/1222387200 320441470156800-320441470156800 [][] 497664497664 1.55911.5591 Γ0(N)\Gamma_0(N)-optimal
125760.cc2 125760bx2 [0,1,0,208575,13730625][0, 1, 0, 208575, -13730625] 3827969464210991/25291023750003827969464210991/2529102375000 662989012992000000-662989012992000000 [][] 14929921492992 2.10842.1084  

Rank

sage: E.rank()
 

The elliptic curves in class 125760.cc have rank 00.

Complex multiplication

The elliptic curves in class 125760.cc do not have complex multiplication.

Modular form 125760.2.a.cc

sage: E.q_eigenform(10)
 
q+q3+q5+q7+q9+4q13+q157q19+O(q20)q + q^{3} + q^{5} + q^{7} + q^{9} + 4 q^{13} + q^{15} - 7 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.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.