Properties

Label 9282l
Number of curves 22
Conductor 92829282
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 9282l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9282.i1 9282l1 [1,0,1,13044382,18132484496][1, 0, 1, -13044382, 18132484496] 245467607504992533120574297/1733763438231552245467607504992533120574297/1733763438231552 17337634382315521733763438231552 [2][2] 349440349440 2.52202.5220 Γ0(N)\Gamma_0(N)-optimal
9282.i2 9282l2 [1,0,1,13036062,18156772240][1, 0, 1, -13036062, 18156772240] 244998212735457942818233177/652408656229361356416-244998212735457942818233177/652408656229361356416 652408656229361356416-652408656229361356416 [2][2] 698880698880 2.86862.8686  

Rank

sage: E.rank()
 

The elliptic curves in class 9282l have rank 00.

Complex multiplication

The elliptic curves in class 9282l do not have complex multiplication.

Modular form 9282.2.a.l

sage: E.q_eigenform(10)
 
qq2+q3+q42q5q6+q7q8+q9+2q102q11+q12+q13q142q15+q16q17q18+8q19+O(q20)q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} - 2 q^{11} + q^{12} + q^{13} - q^{14} - 2 q^{15} + q^{16} - q^{17} - q^{18} + 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 Cremona 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 Cremona labels.