Elliptic curve isogeny class with LMFDB label 59200.cp (Cremona label 59200x)

• Label: 59200.cp
• Number of curves: $3$
• Conductor: $59200$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 59200.cp have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59200.cp do not have complex multiplication.

Modular form 59200.2.a.cp

Isogeny matrix

The \(i,j\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 59200.cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59200.cp1	59200x3	\([0, 1, 0, -187333, -31270787]\)	\(727057727488000/37\)	\(37000000\)	\([]\)	\(124416\)	\(1.3734\)
59200.cp2	59200x2	\([0, 1, 0, -2333, -42787]\)	\(1404928000/50653\)	\(50653000000\)	\([]\)	\(41472\)	\(0.82407\)
59200.cp3	59200x1	\([0, 1, 0, -333, 2213]\)	\(4096000/37\)	\(37000000\)	\([]\)	\(13824\)	\(0.27476\)	\(\Gamma_0(N)\)-optimal