Elliptic curve isogeny class with Cremona label 389136cr (LMFDB label 389136.cr)

• Label: 389136cr
• Number of curves: $2$
• Conductor: $389136$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 389136cr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(67\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 389136cr do not have complex multiplication.

Modular form 389136.2.a.cr

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 389136cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
389136.cr2	389136cr1	\([0, 1, 0, -204288, -31084044]\)	\(129938649625/17924577\)	\(130066356448038912\)	\([2]\)	\(2764800\)	\(2.0106\)	\(\Gamma_0(N)\)-optimal
389136.cr1	389136cr2	\([0, 1, 0, -852848, 271663764]\)	\(9454162623625/1068251283\)	\(7751566586522677248\)	\([2]\)	\(5529600\)	\(2.3572\)