Elliptic curve isogeny class with Cremona label 31200p (LMFDB label 31200.bh)

• Label: 31200p
• Number of curves: $4$
• Conductor: $31200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 31200p have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 31200p do not have complex multiplication.

Modular form 31200.2.a.p

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 31200p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31200.bh3	31200p1	\([0, 1, 0, -406758, -56638512]\)	\(7442744143086784/2927948765625\)	\(2927948765625000000\)	\([2, 2]\)	\(589824\)	\(2.2419\)	\(\Gamma_0(N)\)-optimal
31200.bh4	31200p2	\([0, 1, 0, 1304367, -407419137]\)	\(3834800837445824/3342041015625\)	\(-213890625000000000000\)	\([2]\)	\(1179648\)	\(2.5885\)
31200.bh2	31200p3	\([0, 1, 0, -2938008, 1897486488]\)	\(350584567631475848/8259273550125\)	\(66074188401000000000\)	\([2]\)	\(1179648\)	\(2.5885\)
31200.bh1	31200p4	\([0, 1, 0, -5688008, -5221701012]\)	\(2543984126301795848/909361981125\)	\(7274895849000000000\)	\([2]\)	\(1179648\)	\(2.5885\)