Elliptic curve isogeny class with Cremona label 139650fk (LMFDB label 139650.cu)

• Label: 139650fk
• Number of curves: $2$
• Conductor: $139650$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 139650fk have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 139650fk do not have complex multiplication.

Modular form 139650.2.a.fk

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 139650fk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139650.cu1	139650fk1	\([1, 0, 1, -973901, 369910748]\)	\(-1389310279182025/267418692\)	\(-19663463559442500\)	\([]\)	\(2592000\)	\(2.1269\)	\(\Gamma_0(N)\)-optimal
139650.cu2	139650fk2	\([1, 0, 1, 5845674, -323404952]\)	\(480705753733655/279172334592\)	\(-12829822653286800000000\)	\([]\)	\(12960000\)	\(2.9316\)