Properties

Label 357.c
Number of curves 11
Conductor 357357
CM no
Rank 11

Related objects

Downloads

Learn more

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 357.c1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
331+T1 + T
771T1 - T
17171T1 - T
 
Good L-factors:
Prime L-Factor Isogeny Class over Fp\mathbb{F}_p
22 1+2T2 1 + 2 T^{2} 1.2.a
55 1T+5T2 1 - T + 5 T^{2} 1.5.ab
1111 1+5T+11T2 1 + 5 T + 11 T^{2} 1.11.f
1313 1+5T+13T2 1 + 5 T + 13 T^{2} 1.13.f
1919 1+5T+19T2 1 + 5 T + 19 T^{2} 1.19.f
2323 1+T+23T2 1 + T + 23 T^{2} 1.23.b
2929 1+6T+29T2 1 + 6 T + 29 T^{2} 1.29.g
\cdots\cdots\cdots
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 357.c do not have complex multiplication.

Modular form 357.2.a.c

Copy content sage:E.q_eigenform(10)
 
qq32q4+q5+q7+q95q11+2q125q13q15+4q16+q175q19+O(q20)q - q^{3} - 2 q^{4} + q^{5} + q^{7} + q^{9} - 5 q^{11} + 2 q^{12} - 5 q^{13} - q^{15} + 4 q^{16} + q^{17} - 5 q^{19} + O(q^{20}) Copy content Toggle raw display

Elliptic curves in class 357.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
357.c1 357b1 [0,1,1,5,16][0, -1, 1, -5, -16] 16777216/122451-16777216/122451 122451-122451 [][] 3232 0.34061-0.34061 Γ0(N)\Gamma_0(N)-optimal