Properties

Label 346560.hw
Number of curves 22
Conductor 346560346560
CM no
Rank 11
Graph

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Copy content sage:E = EllipticCurve("hw1") E.isogeny_class()
 

Elliptic curves in class 346560.hw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.hw1 346560hw2 [0,1,0,69261,6992829][0, 1, 0, -69261, 6992829] 1590409933520896/451590409933520896/45 10396801039680 [][] 559872559872 1.11511.1151  
346560.hw2 346560hw1 [0,1,0,861,9189][0, 1, 0, -861, 9189] 3058794496/911253058794496/91125 21053520002105352000 [][] 186624186624 0.565820.56582 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 346560.hw have rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
331T1 - T
551+T1 + T
191911
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
77 12T+7T2 1 - 2 T + 7 T^{2} 1.7.ac
1111 13T+11T2 1 - 3 T + 11 T^{2} 1.11.ad
1313 1+4T+13T2 1 + 4 T + 13 T^{2} 1.13.e
1717 1+17T2 1 + 17 T^{2} 1.17.a
2323 1+6T+23T2 1 + 6 T + 23 T^{2} 1.23.g
2929 13T+29T2 1 - 3 T + 29 T^{2} 1.29.ad
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 346560.hw do not have complex multiplication.

Modular form 346560.2.a.hw

Copy content sage:E.q_eigenform(10)
 
q+q3q5+2q7+q9+3q114q13q15+O(q20)q + q^{3} - q^{5} + 2 q^{7} + q^{9} + 3 q^{11} - 4 q^{13} - q^{15} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.