Elliptic curve isogeny class with Cremona label 121968fu (LMFDB label 121968.fb)

• Label: 121968fu
• Number of curves: $4$
• Conductor: $121968$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 121968fu have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 121968.2.a.fu

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 121968fu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121968.fb4	121968fu1	\([0, 0, 0, 60621, 3500530]\)	\(4657463/3696\)	\(-19551295952584704\)	\([2]\)	\(737280\)	\(1.8139\)	\(\Gamma_0(N)\)-optimal
121968.fb3	121968fu2	\([0, 0, 0, -287859, 30333490]\)	\(498677257/213444\)	\(1129087341261766656\)	\([2, 2]\)	\(1474560\)	\(2.1605\)
121968.fb2	121968fu3	\([0, 0, 0, -2204499, -1238865518]\)	\(223980311017/4278582\)	\(22633068977110867968\)	\([2]\)	\(2949120\)	\(2.5071\)
121968.fb1	121968fu4	\([0, 0, 0, -3946899, 3016841938]\)	\(1285429208617/614922\)	\(3252846864111280128\)	\([2]\)	\(2949120\)	\(2.5071\)