Elliptic curve isogeny class with LMFDB label 317130.bh (Cremona label 317130bh)

• Label: 317130.bh
• Number of curves: $4$
• Conductor: $317130$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 317130.bh have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(11\)	\(1 + T\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 317130.bh do not have complex multiplication.

Modular form 317130.2.a.bh

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 317130.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
317130.bh1	317130bh4	\([1, 0, 1, -1540023, -735717122]\)	\(455129268177961/4392300\)	\(3898182418056300\)	\([2]\)	\(7372800\)	\(2.1530\)
317130.bh2	317130bh2	\([1, 0, 1, -98523, -10930922]\)	\(119168121961/10890000\)	\(9664915086090000\)	\([2, 2]\)	\(3686400\)	\(1.8064\)
317130.bh3	317130bh1	\([1, 0, 1, -21643, 1031606]\)	\(1263214441/211200\)	\(187440777427200\)	\([2]\)	\(1843200\)	\(1.4598\)	\(\Gamma_0(N)\)-optimal
317130.bh4	317130bh3	\([1, 0, 1, 112897, -51438994]\)	\(179310732119/1392187500\)	\(-1235571530892187500\)	\([2]\)	\(7372800\)	\(2.1530\)