Elliptic curve isogeny class with Cremona label 242064ca (LMFDB label 242064.ca)

• Label: 242064ca
• Number of curves: $2$
• Conductor: $242064$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 242064ca have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 242064ca do not have complex multiplication.

Modular form 242064.2.a.ca

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 242064ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
242064.ca1	242064ca1	\([0, 0, 0, -109872007419, -14017762246464470]\)	\(10341755683137709164937/356992303104\)	\(5063484317783854583409278976\)	\([2]\)	\(541900800\)	\(4.8136\)	\(\Gamma_0(N)\)-optimal
242064.ca2	242064ca2	\([0, 0, 0, -109717086459, -14059263371770838]\)	\(-10298071306410575356297/60769798505543808\)	\(-861942733925173031329109654372352\)	\([2]\)	\(1083801600\)	\(5.1602\)