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Properties

Label 293046.s
Number of curves $1$
Conductor $293046$
CM no
Rank $1$

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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 293046.s1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(13\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(7\) \( 1 + 3 T + 7 T^{2}\) 1.7.d
\(11\) \( 1 + 2 T + 11 T^{2}\) 1.11.c
\(19\) \( 1 + 7 T + 19 T^{2}\) 1.19.h
\(23\) \( 1 + 9 T + 23 T^{2}\) 1.23.j
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 293046.s do not have complex multiplication.

Modular form 293046.2.a.s

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

Elliptic curves in class 293046.s

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
293046.s1 293046s1 \([1, 0, 1, -4497378721294, -3618910951154612800]\) \(298779371619116129414560801/4874288601508740071424\) \(164120459641669708301374305871966765056\) \([]\) \(14975767296\) \(6.1320\) \(\Gamma_0(N)\)-optimal