Properties

Label 356928h
Number of curves $1$
Conductor $356928$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("h1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 356928h1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(11\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 3 T + 5 T^{2}\) 1.5.d
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(17\) \( 1 - 7 T + 17 T^{2}\) 1.17.ah
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 356928h do not have complex multiplication.

Modular form 356928.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - q^{7} + q^{9} - q^{11} + 3 q^{15} + 7 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 356928h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
356928.h1 356928h1 \([0, -1, 0, -319297, 97713121]\) \(-16835377/9504\) \(-2032325039851831296\) \([]\) \(7188480\) \(2.2161\) \(\Gamma_0(N)\)-optimal