Properties

Label 293046.bq
Number of curves $1$
Conductor $293046$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 293046.bq1 has rank \(0\).

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 \(\mathbb{F}_p\)
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 293046.2.a.bq

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

Elliptic curves in class 293046.bq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
293046.bq1 293046bq1 \([1, 1, 1, -3623596688, 85036443297905]\) \(-3772118414306118217515625/56562751486929272832\) \(-78902085805201469379527442432\) \([]\) \(449305920\) \(4.3481\) \(\Gamma_0(N)\)-optimal