↑

Properties

Label 350350dq
Number of curves $1$
Conductor $350350$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("dq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 350350dq1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
\(11\)\(1 + T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 3 T + 3 T^{2}\) 1.3.ad
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 3 T + 19 T^{2}\) 1.19.ad
\(23\) \( 1 + 9 T + 23 T^{2}\) 1.23.j
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 350350dq do not have complex multiplication.

Modular form 350350.2.a.dq

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

Elliptic curves in class 350350dq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350350.dq1 350350dq1 \([1, -1, 0, -399488287, 3073440948941]\) \(-117463704966052899285072465/2057109481887629312\) \(-123477996650304949452800\) \([]\) \(166997376\) \(3.5590\) \(\Gamma_0(N)\)-optimal