Properties

Label 1530.h
Number of curves 22
Conductor 15301530
CM no
Rank 00
Graph

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

Elliptic curves in class 1530.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1530.h1 1530h2 [1,1,0,1404,17690][1, -1, 0, -1404, -17690] 420021471169/50191650420021471169/50191650 3658971285036589712850 [2][2] 12801280 0.757860.75786  
1530.h2 1530h1 [1,1,0,126,1472][1, -1, 0, 126, -1472] 302111711/1404540302111711/1404540 1023909660-1023909660 [2][2] 640640 0.411280.41128 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1530.h have rank 00.

Complex multiplication

The elliptic curves in class 1530.h do not have complex multiplication.

Modular form 1530.2.a.h

sage: E.q_eigenform(10)
 
qq2+q4+q5+2q7q8q10+4q132q14+q16+q17+4q19+O(q20)q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} + 4 q^{13} - 2 q^{14} + q^{16} + 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.