Elliptic curve isogeny class with LMFDB label 14706.v (Cremona label 14706p)

• Label: 14706.v
• Number of curves: $2$
• Conductor: $14706$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 14706.v have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(19\)	\(1 + T\)
\(43\)	\(1 - T\)

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 14706.v do not have complex multiplication.

Modular form 14706.2.a.v

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 14706.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
14706.v1	14706p2	\([1, -1, 1, -78629, 842343]\)	\(73746134776499977/42276087308934\)	\(30819267648212886\)	\([2]\)	\(107520\)	\(1.8536\)
14706.v2	14706p1	\([1, -1, 1, -56759, 5207595]\)	\(27739154300781097/69662939652\)	\(50784283006308\)	\([2]\)	\(53760\)	\(1.5070\)	\(\Gamma_0(N)\)-optimal