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

• Label: 39216.a
• Number of curves: $2$
• Conductor: $39216$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 39216.a 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 39216.2.a.a

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 39216.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
39216.a1	39216o1	\([0, -1, 0, -2146560, -272646144]\)	\(267050295730790058241/146661674185654272\)	\(600726217464439898112\)	\([2]\)	\(1827840\)	\(2.6777\)	\(\Gamma_0(N)\)-optimal
39216.a2	39216o2	\([0, -1, 0, 8339200, -2160082944]\)	\(15658021359810921772799/9552201996027691008\)	\(-39125819375729422368768\)	\([2]\)	\(3655680\)	\(3.0243\)