Elliptic curve isogeny class with Cremona label 14994bf (LMFDB label 14994.bf)

• Label: 14994bf
• Number of curves: $4$
• Conductor: $14994$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 14994bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 14994bf do not have complex multiplication.

Modular form 14994.2.a.bf

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 14994bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14994.bf3	14994bf1	\([1, -1, 0, -8241, 285389]\)	\(721734273/13328\)	\(1143090860688\)	\([2]\)	\(24576\)	\(1.1082\)	\(\Gamma_0(N)\)-optimal
14994.bf2	14994bf2	\([1, -1, 0, -17061, -425503]\)	\(6403769793/2775556\)	\(238048671738276\)	\([2, 2]\)	\(49152\)	\(1.4548\)
14994.bf1	14994bf3	\([1, -1, 0, -233151, -43254541]\)	\(16342588257633/8185058\)	\(702000674820018\)	\([2]\)	\(98304\)	\(1.8014\)
14994.bf4	14994bf4	\([1, -1, 0, 57909, -3199393]\)	\(250404380127/196003234\)	\(-16810437083635314\)	\([2]\)	\(98304\)	\(1.8014\)