Elliptic curve isogeny class with LMFDB label 5200.d (Cremona label 5200bb)

• Label: 5200.d
• Number of curves: $2$
• Conductor: $5200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 5200.d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5200.d do not have complex multiplication.

Modular form 5200.2.a.d

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 5200.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5200.d1	5200bb1	\([0, 1, 0, -408, -812]\)	\(117649/65\)	\(4160000000\)	\([2]\)	\(3072\)	\(0.53625\)	\(\Gamma_0(N)\)-optimal
5200.d2	5200bb2	\([0, 1, 0, 1592, -4812]\)	\(6967871/4225\)	\(-270400000000\)	\([2]\)	\(6144\)	\(0.88282\)