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Properties

Label 232050.gx
Number of curves $1$
Conductor $232050$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 232050.gx1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1 + T\)
\(13\)\(1 - T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 6 T + 11 T^{2}\) 1.11.ag
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 8 T + 29 T^{2}\) 1.29.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 232050.gx do not have complex multiplication.

Modular form 232050.2.a.gx

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + 6 q^{11} + q^{12} + q^{13} - q^{14} + q^{16} - q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 232050.gx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232050.gx1 232050gx1 \([1, 0, 0, -741713, -245930583]\) \(-2888094474031216969/10826524800\) \(-169164450000000\) \([]\) \(3386880\) \(1.9454\) \(\Gamma_0(N)\)-optimal