Elliptic curve isogeny class with Cremona label 121968cc (LMFDB label 121968.bq)

• Label: 121968cc
• Number of curves: $2$
• Conductor: $121968$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 121968cc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121968cc do not have complex multiplication.

Modular form 121968.2.a.cc

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 121968cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121968.bq2	121968cc1	\([0, 0, 0, 4168329, -3472374026]\)	\(24226243449392/29774625727\)	\(-9843961706338262646528\)	\([2]\)	\(5529600\)	\(2.9062\)	\(\Gamma_0(N)\)-optimal
121968.bq1	121968cc2	\([0, 0, 0, -24820851, -33383409950]\)	\(1278763167594532/375974556419\)	\(497212515096700767243264\)	\([2]\)	\(11059200\)	\(3.2528\)