Elliptic curve isogeny class with LMFDB label 388416.fn (Cremona label 388416fn)

• Label: 388416.fn
• Number of curves: $4$
• Conductor: $388416$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 388416.fn have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388416.fn do not have complex multiplication.

Modular form 388416.2.a.fn

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 388416.fn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388416.fn1	388416fn4	\([0, 1, 0, -146377729, -588577138273]\)	\(438536015880092936/64602489661101\)	\(51096684192288342129672192\)	\([2]\)	\(84934656\)	\(3.6577\)
388416.fn2	388416fn2	\([0, 1, 0, -39320569, 85818735431]\)	\(68003243639904448/7163272192041\)	\(708214688977595958595584\)	\([2, 2]\)	\(42467328\)	\(3.3112\)
388416.fn3	388416fn1	\([0, 1, 0, -38267164, 91100718782]\)	\(4011705594213827392/52680152007\)	\(81380531455964862912\)	\([2]\)	\(21233664\)	\(2.9646\)	\(\Gamma_0(N)\)-optimal
388416.fn4	388416fn3	\([0, 1, 0, 50882111, 422184529151]\)	\(18419405270942584/108003564029403\)	\(-85424323920056580220747776\)	\([2]\)	\(84934656\)	\(3.6577\)