Elliptic curve isogeny class with LMFDB label 17472.bg (Cremona label 17472a)

• Label: 17472.bg
• Number of curves: $4$
• Conductor: $17472$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 17472.bg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17472.bg do not have complex multiplication.

Modular form 17472.2.a.bg

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 17472.bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17472.bg1	17472a3	\([0, -1, 0, -125217, 17093025]\)	\(828279937799497/193444524\)	\(50710321299456\)	\([2]\)	\(73728\)	\(1.6204\)
17472.bg2	17472a2	\([0, -1, 0, -8737, 203425]\)	\(281397674377/96589584\)	\(25320379908096\)	\([2, 2]\)	\(36864\)	\(1.2738\)
17472.bg3	17472a1	\([0, -1, 0, -3617, -80223]\)	\(19968681097/628992\)	\(164886478848\)	\([2]\)	\(18432\)	\(0.92722\)	\(\Gamma_0(N)\)-optimal
17472.bg4	17472a4	\([0, -1, 0, 25823, 1385377]\)	\(7264187703863/7406095788\)	\(-1941463574249472\)	\([2]\)	\(73728\)	\(1.6204\)