Properties

Label 145728.h
Number of curves 22
Conductor 145728145728
CM no
Rank 22
Graph

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

Elliptic curves in class 145728.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145728.h1 145728ea2 [0,0,0,367932,85447600][0, 0, 0, -367932, 85447600] 461188987116496/2811467307461188987116496/2811467307 3357998558090035233579985580900352 [2][2] 14745601474560 2.00982.0098  
145728.h2 145728ea1 [0,0,0,367392,85712200][0, 0, 0, -367392, 85712200] 7346581704933376/2755177346581704933376/275517 205672338432205672338432 [2][2] 737280737280 1.66321.6632 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145728.h have rank 22.

Complex multiplication

The elliptic curves in class 145728.h do not have complex multiplication.

Modular form 145728.2.a.h

sage: E.q_eigenform(10)
 
q4q5+q11+2q132q174q19+O(q20)q - 4 q^{5} + q^{11} + 2 q^{13} - 2 q^{17} - 4 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.