Elliptic curve isogeny class with LMFDB label 331200.bp (Cremona label 331200bp)

• Label: 331200.bp
• Number of curves: $4$
• Conductor: $331200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 331200.bp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 331200.bp do not have complex multiplication.

Modular form 331200.2.a.bp

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 331200.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
331200.bp1	331200bp3	\([0, 0, 0, -677100, 181474000]\)	\(45989074372/7555707\)	\(5640305052672000000\)	\([2]\)	\(6291456\)	\(2.3197\)
331200.bp2	331200bp2	\([0, 0, 0, -191100, -29450000]\)	\(4135597648/385641\)	\(71969865984000000\)	\([2, 2]\)	\(3145728\)	\(1.9731\)
331200.bp3	331200bp1	\([0, 0, 0, -186600, -31025000]\)	\(61604313088/621\)	\(7243344000000\)	\([2]\)	\(1572864\)	\(1.6265\)	\(\Gamma_0(N)\)-optimal
331200.bp4	331200bp4	\([0, 0, 0, 222900, -139574000]\)	\(1640689628/12223143\)	\(-9124527356928000000\)	\([2]\)	\(6291456\)	\(2.3197\)