Elliptic curve isogeny class with LMFDB label 143344.d (Cremona label 143344b)

• Label: 143344.d
• Number of curves: $2$
• Conductor: $143344$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 143344.d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(17\)	\(1\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 143344.d do not have complex multiplication.

Modular form 143344.2.a.d

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 143344.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
143344.d1	143344b1	\([0, 1, 0, -674, -8777]\)	\(-87808/31\)	\(-11972234224\)	\([]\)	\(110592\)	\(0.64485\)	\(\Gamma_0(N)\)-optimal
143344.d2	143344b2	\([0, 1, 0, 5106, 84859]\)	\(38112512/29791\)	\(-11505317089264\)	\([]\)	\(331776\)	\(1.1942\)