Properties

Label 7488.bv
Number of curves 22
Conductor 74887488
CM no
Rank 11
Graph

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Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Elliptic curves in class 7488.bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.bv1 7488z2 [0,0,0,104484,12995552][0, 0, 0, -104484, 12995552] 42246001231552/1441451742246001231552/14414517 4304151712972843041517129728 [2][2] 2457624576 1.58771.5877  
7488.bv2 7488z1 [0,0,0,5619,261740][0, 0, 0, -5619, 261740] 420526439488/390971529-420526439488/390971529 18241167657024-18241167657024 [2][2] 1228812288 1.24111.2411 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 7488.bv have rank 11.

Complex multiplication

The elliptic curves in class 7488.bv do not have complex multiplication.

Modular form 7488.2.a.bv

Copy content sage:E.q_eigenform(10)
 
q+2q5+2q72q11+q136q172q19+O(q20)q + 2 q^{5} + 2 q^{7} - 2 q^{11} + q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.