Properties

Label 22344n
Number of curves $1$
Conductor $22344$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("n1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 22344n1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(7\)\(1\)
\(19\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 5 T + 17 T^{2}\) 1.17.af
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 22344n do not have complex multiplication.

Modular form 22344.2.a.n

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} + q^{9} + 3 q^{11} + 4 q^{13} + 3 q^{15} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 22344n

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22344.bi1 22344n1 \([0, 1, 0, -30984, 2089968]\) \(-669003004754/390963\) \(-1922462029824\) \([]\) \(53760\) \(1.3022\) \(\Gamma_0(N)\)-optimal