Properties

Label 4368.y
Number of curves 44
Conductor 43684368
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 4368.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.y1 4368m4 [0,1,0,13592,605412][0, 1, 0, -13592, 605412] 271210066309732/51597271210066309732/51597 5283532852835328 [4][4] 40964096 0.874030.87403  
4368.y2 4368m3 [0,1,0,1632,11100][0, 1, 0, -1632, -11100] 469732169092/224827239469732169092/224827239 230223092736230223092736 [2][2] 40964096 0.874030.87403  
4368.y3 4368m2 [0,1,0,852,9180][0, 1, 0, -852, 9180] 267492843088/3651921267492843088/3651921 934891776934891776 [2,2][2, 2] 20482048 0.527460.52746  
4368.y4 4368m1 [0,1,0,7,392][0, 1, 0, -7, 392] 2725888/4198467-2725888/4198467 67175472-67175472 [2][2] 10241024 0.180890.18089 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4368.y have rank 00.

Complex multiplication

The elliptic curves in class 4368.y do not have complex multiplication.

Modular form 4368.2.a.y

sage: E.q_eigenform(10)
 
q+q3+2q5+q7+q9+q13+2q156q17+4q19+O(q20)q + q^{3} + 2 q^{5} + q^{7} + q^{9} + q^{13} + 2 q^{15} - 6 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.

(1424412422124421)\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.