Properties

Label 1575.h
Number of curves 44
Conductor 15751575
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 1575.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1575.h1 1575f3 [1,1,0,25317,1556716][1, -1, 0, -25317, 1556716] 157551496201/13125157551496201/13125 149501953125149501953125 [2][2] 30723072 1.18811.1881  
1575.h2 1575f2 [1,1,0,1692,21091][1, -1, 0, -1692, 21091] 47045881/1102547045881/11025 125581640625125581640625 [2,2][2, 2] 15361536 0.841490.84149  
1575.h3 1575f1 [1,1,0,567,4784][1, -1, 0, -567, -4784] 1771561/1051771561/105 11960156251196015625 [2][2] 768768 0.494920.49492 Γ0(N)\Gamma_0(N)-optimal
1575.h4 1575f4 [1,1,0,3933,127966][1, -1, 0, 3933, 127966] 590589719/972405590589719/972405 11076300703125-11076300703125 [2][2] 30723072 1.18811.1881  

Rank

sage: E.rank()
 

The elliptic curves in class 1575.h have rank 00.

Complex multiplication

The elliptic curves in class 1575.h do not have complex multiplication.

Modular form 1575.2.a.h

sage: E.q_eigenform(10)
 
q+q2q4q73q8+6q13q14q16+2q178q19+O(q20)q + q^{2} - q^{4} - q^{7} - 3 q^{8} + 6 q^{13} - q^{14} - q^{16} + 2 q^{17} - 8 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.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.