Properties

Label 360672.q
Number of curves $1$
Conductor $360672$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 360672.q1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(13\)\(1 + T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - T + 5 T^{2}\) 1.5.ab
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(19\) \( 1 - 7 T + 19 T^{2}\) 1.19.ah
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 + 8 T + 29 T^{2}\) 1.29.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 360672.q do not have complex multiplication.

Modular form 360672.2.a.q

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 3 q^{7} + q^{9} - 4 q^{11} - q^{13} - q^{15} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 360672.q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
360672.q1 360672q1 \([0, -1, 0, -19425, -1035567]\) \(684811998784/28431\) \(33655025664\) \([]\) \(709632\) \(1.1009\) \(\Gamma_0(N)\)-optimal