Properties

Label 33120o
Number of curves 11
Conductor 3312033120
CM no
Rank 11

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Show commands: SageMath
Copy content sage:E = EllipticCurve("o1") E.isogeny_class()
 

Elliptic curves in class 33120o

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33120.x1 33120o1 [0,0,0,888,2563216][0, 0, 0, 888, -2563216] 25934336/95054687525934336/950546875 2838317760000000-2838317760000000 [][] 9676896768 1.64411.6441 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 33120o1 has rank 11.

L-function data

 
Bad L-factors:
Prime L-Factor
2211
3311
551+T1 + T
23231+T1 + T
 
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 16T+11T2 1 - 6 T + 11 T^{2} 1.11.ag
1313 12T+13T2 1 - 2 T + 13 T^{2} 1.13.ac
1717 14T+17T2 1 - 4 T + 17 T^{2} 1.17.ae
1919 1+8T+19T2 1 + 8 T + 19 T^{2} 1.19.i
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 33120o do not have complex multiplication.

Modular form 33120.2.a.o

Copy content sage:E.q_eigenform(10)
 
q+q5q7+2q11+q17+4q19+O(q20)q + q^{5} - q^{7} + 2 q^{11} + q^{17} + 4 q^{19} + O(q^{20}) Copy content Toggle raw display