Properties

Label 5415c
Number of curves 22
Conductor 54155415
CM no
Rank 22
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("c1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 5415c have rank 22.

L-function data

 
Bad L-factors:
Prime L-Factor
331T1 - T
551+T1 + T
191911
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
22 1+T+2T2 1 + T + 2 T^{2} 1.2.b
77 1+2T+7T2 1 + 2 T + 7 T^{2} 1.7.c
1111 1+2T+11T2 1 + 2 T + 11 T^{2} 1.11.c
1313 14T+13T2 1 - 4 T + 13 T^{2} 1.13.ae
1717 12T+17T2 1 - 2 T + 17 T^{2} 1.17.ac
2323 1+4T+23T2 1 + 4 T + 23 T^{2} 1.23.e
2929 1+4T+29T2 1 + 4 T + 29 T^{2} 1.29.e
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 5415c do not have complex multiplication.

Modular form 5415.2.a.c

Copy content sage:E.q_eigenform(10)
 
q+q2q3q4q5q62q73q8+q9q106q11+q122q14+q15q166q17+q18+O(q20)q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 2 q^{7} - 3 q^{8} + q^{9} - q^{10} - 6 q^{11} + q^{12} - 2 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} + 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 Cremona numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 5415c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.h2 5415c1 [1,1,0,6852,13707][1, 1, 0, 6852, 13707] 756058031/438615756058031/438615 20635029094815-20635029094815 [2][2] 1440014400 1.24431.2443 Γ0(N)\Gamma_0(N)-optimal
5415.h1 5415c2 [1,1,0,27443,75438][1, 1, 0, -27443, 75438] 48587168449/2804827548587168449/28048275 13195558079052751319555807905275 [2][2] 2880028800 1.59091.5909