Elliptic curve isogeny class with Cremona label 39216i (LMFDB label 39216.i)

• Label: 39216i
• Number of curves: $4$
• Conductor: $39216$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 39216i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(19\)	\(1 + T\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 39216i do not have complex multiplication.

Modular form 39216.2.a.i

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 39216i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
39216.i2	39216i1	\([0, -1, 0, -96008, -11395344]\)	\(23894093340015625/55042322688\)	\(225453353730048\)	\([2]\)	\(165888\)	\(1.6351\)	\(\Gamma_0(N)\)-optimal
39216.i3	39216i2	\([0, -1, 0, -61448, -19745040]\)	\(-6264610702863625/37578744274608\)	\(-153922536548794368\)	\([2]\)	\(331776\)	\(1.9817\)
39216.i1	39216i3	\([0, -1, 0, -438008, 101568624]\)	\(2268876641163765625/228097945239552\)	\(934289183701204992\)	\([2]\)	\(497664\)	\(2.1844\)
39216.i4	39216i4	\([0, -1, 0, 545032, 491638896]\)	\(4371484788393482375/28041364201746432\)	\(-114857427770353385472\)	\([2]\)	\(995328\)	\(2.5310\)