Elliptic curve isogeny class with Cremona label 200376bh (LMFDB label 200376.w)

• Label: 200376bh
• Number of curves: $2$
• Conductor: $200376$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 200376bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 200376bh do not have complex multiplication.

Modular form 200376.2.a.bh

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 200376bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
200376.w2	200376bh1	\([0, 0, 0, 5445, 215622]\)	\(13500/23\)	\(-30416653605888\)	\([2]\)	\(414720\)	\(1.2721\)	\(\Gamma_0(N)\)-optimal
200376.w1	200376bh2	\([0, 0, 0, -38115, 2228094]\)	\(2315250/529\)	\(1399166065870848\)	\([2]\)	\(829440\)	\(1.6187\)