Elliptic curve isogeny class with LMFDB label 171600.ft (Cremona label 171600bt)

• Label: 171600.ft
• Number of curves: $4$
• Conductor: $171600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 171600.ft have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 171600.ft do not have complex multiplication.

Modular form 171600.2.a.ft

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 171600.ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171600.ft1	171600bt4	\([0, 1, 0, -10561408, -13214372812]\)	\(2035678735521204409/141376950\)	\(9048124800000000\)	\([2]\)	\(3538944\)	\(2.5159\)
171600.ft2	171600bt3	\([0, 1, 0, -1129408, 122763188]\)	\(2489411558640889/1338278906250\)	\(85649850000000000000\)	\([2]\)	\(3538944\)	\(2.5159\)
171600.ft3	171600bt2	\([0, 1, 0, -661408, -205772812]\)	\(499980107400409/4140922500\)	\(265019040000000000\)	\([2, 2]\)	\(1769472\)	\(2.1693\)
171600.ft4	171600bt1	\([0, 1, 0, -13408, -7484812]\)	\(-4165509529/375289200\)	\(-24018508800000000\)	\([2]\)	\(884736\)	\(1.8227\)	\(\Gamma_0(N)\)-optimal