Properties

Label 371943q
Number of curves $1$
Conductor $371943$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("q1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 371943q1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1\)
\(11\)\(1 - T\)
\(13\)\(1 + T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(5\) \( 1 - 4 T + 5 T^{2}\) 1.5.ae
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 371943q do not have complex multiplication.

Modular form 371943.2.a.q

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

Elliptic curves in class 371943q

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
371943.q1 371943q1 \([1, -1, 1, 94882, -8806476]\) \(18576359/17303\) \(-87991416100183167\) \([]\) \(4406400\) \(1.9386\) \(\Gamma_0(N)\)-optimal