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

• Label: 39216.b
• Number of curves: $2$
• Conductor: $39216$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 39216.b have rank \(1\).

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
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 39216.2.a.b

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.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
39216.b1	39216r1	\([0, -1, 0, -2440, -45584]\)	\(392383937161/29412\)	\(120471552\)	\([2]\)	\(39936\)	\(0.60000\)	\(\Gamma_0(N)\)-optimal
39216.b2	39216r2	\([0, -1, 0, -2280, -51984]\)	\(-320153881321/108133218\)	\(-442913660928\)	\([2]\)	\(79872\)	\(0.94657\)