Elliptic curve isogeny class with LMFDB label 155232.ei (Cremona label 155232bz)

• Label: 155232.ei
• Number of curves: $4$
• Conductor: $155232$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 155232.ei have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 155232.ei do not have complex multiplication.

Modular form 155232.2.a.ei

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 155232.ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
155232.ei1	155232bz4	\([0, 0, 0, -3182844, -2181995872]\)	\(10150654719808/19370043\)	\(6804657978217279488\)	\([2]\)	\(3538944\)	\(2.5032\)
155232.ei2	155232bz2	\([0, 0, 0, -2642619, 1644655502]\)	\(46477380430664/286446699\)	\(12578520190200104448\)	\([2]\)	\(3538944\)	\(2.5032\)
155232.ei3	155232bz1	\([0, 0, 0, -265629, -9254140]\)	\(377619516352/211789809\)	\(1162520984656696896\)	\([2, 2]\)	\(1769472\)	\(2.1566\)	\(\Gamma_0(N)\)-optimal
155232.ei4	155232bz3	\([0, 0, 0, 1044141, -73432870]\)	\(2866919053816/1712145897\)	\(-75184185431938834944\)	\([2]\)	\(3538944\)	\(2.5032\)