Properties

Label 29400v
Number of curves $1$
Conductor $29400$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("v1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 29400v1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - 3 T + 19 T^{2}\) 1.19.ad
\(23\) \( 1 + 9 T + 23 T^{2}\) 1.23.j
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29400v do not have complex multiplication.

Modular form 29400.2.a.v

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{13} - 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 29400v

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.bd1 29400v1 \([0, -1, 0, -1841583, -982059588]\) \(-46028377077760/1162261467\) \(-17441186139168750000\) \([]\) \(547200\) \(2.4762\) \(\Gamma_0(N)\)-optimal