Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 371943bd1 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.ab
\(5\) \( 1 + 5 T^{2}\) 1.5.a
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 371943.2.a.bd

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

Elliptic curves in class 371943bd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
371943.bd1 371943bd1 \([1, -1, 0, -90222, -10535635]\) \(-170953875/2431\) \(-1154967542394237\) \([]\) \(1327104\) \(1.6955\) \(\Gamma_0(N)\)-optimal