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Properties

Label 5950.s
Number of curves $1$
Conductor $5950$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("s1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 5950.s1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1 - T\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 2 T + 3 T^{2}\) 1.3.ac
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(19\) \( 1 - 5 T + 19 T^{2}\) 1.19.af
\(23\) \( 1 - 2 T + 23 T^{2}\) 1.23.ac
\(29\) \( 1 + 5 T + 29 T^{2}\) 1.29.f
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 5950.s do not have complex multiplication.

Modular form 5950.2.a.s

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{7} + q^{8} + q^{9} + 5 q^{11} + 2 q^{12} + 6 q^{13} + q^{14} + q^{16} + q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 5950.s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5950.s1 5950q1 \([1, 1, 1, -13, -29]\) \(-9765625/3808\) \(-95200\) \([]\) \(960\) \(-0.33547\) \(\Gamma_0(N)\)-optimal