Properties

Label 35550ba
Number of curves $1$
Conductor $35550$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("ba1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 35550ba1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1\)
\(5\)\(1\)
\(79\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 35550ba do not have complex multiplication.

Modular form 35550.2.a.ba

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 4 q^{7} - q^{8} + 5 q^{13} + 4 q^{14} + q^{16} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 35550ba

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35550.c1 35550ba1 \([1, -1, 0, 4383, 701541]\) \(6539203/153576\) \(-218665828125000\) \([]\) \(172800\) \(1.4318\) \(\Gamma_0(N)\)-optimal