Elliptic curve isogeny class with Cremona label 143325br (LMFDB label 143325.cb)

• Label: 143325br
• Number of curves: $4$
• Conductor: $143325$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 143325br have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 143325br do not have complex multiplication.

Modular form 143325.2.a.br

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 143325br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
143325.cb3	143325br1	\([1, -1, 1, -11256755, -14392154878]\)	\(117713838907729/1322517105\)	\(1772299407062495390625\)	\([2]\)	\(7962624\)	\(2.8910\)	\(\Gamma_0(N)\)-optimal
143325.cb2	143325br2	\([1, -1, 1, -20572880, 12885459122]\)	\(718576775407009/362361861225\)	\(485599550556383722265625\)	\([2, 2]\)	\(15925248\)	\(3.2376\)
143325.cb1	143325br3	\([1, -1, 1, -266375255, 1672051490372]\)	\(1559802282754777489/1481059636875\)	\(1984761562881832998046875\)	\([2]\)	\(31850496\)	\(3.5842\)
143325.cb4	143325br4	\([1, -1, 1, 76171495, 99374930372]\)	\(36472485598112591/24291459037755\)	\(-32552878360916232786796875\)	\([2]\)	\(31850496\)	\(3.5842\)