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Properties

Label 157170.cs
Number of curves $1$
Conductor $157170$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 157170.cs1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(13\)\(1\)
\(31\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 2 T + 7 T^{2}\) 1.7.ac
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(17\) \( 1 + 17 T^{2}\) 1.17.a
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 + 3 T + 23 T^{2}\) 1.23.d
\(29\) \( 1 + 3 T + 29 T^{2}\) 1.29.d
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 157170.cs do not have complex multiplication.

Modular form 157170.2.a.cs

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2 q^{14} - q^{15} + q^{16} + q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 157170.cs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157170.cs1 157170x1 \([1, 0, 0, 280313114, 3991346954360]\) \(504654146753383024121879/1717841617468945312500\) \(-8291693379773662454882812500\) \([]\) \(105557760\) \(4.0401\) \(\Gamma_0(N)\)-optimal