Elliptic curve isogeny class with LMFDB label 358974.bi (Cremona label 358974bi)

• Label: 358974.bi
• Number of curves: $4$
• Conductor: $358974$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 358974.bi have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 358974.bi do not have complex multiplication.

Modular form 358974.2.a.bi

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 358974.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
358974.bi1	358974bi4	\([1, -1, 0, -476543727, -4003956286583]\)	\(139545621883503188502625/220644468\)	\(18923820140468628\)	\([2]\)	\(47775744\)	\(3.2800\)
358974.bi2	358974bi3	\([1, -1, 0, -29784267, -62554978571]\)	\(34069730739753390625/1354703543952\)	\(116187668069716050192\)	\([2]\)	\(23887872\)	\(2.9334\)
358974.bi3	358974bi2	\([1, -1, 0, -5899707, -5458821467]\)	\(264788619837198625/3058196150592\)	\(262289621093407693632\)	\([2]\)	\(15925248\)	\(2.7307\)
358974.bi4	358974bi1	\([1, -1, 0, -678267, 79037797]\)	\(402355893390625/201513996288\)	\(17283073788830158848\)	\([2]\)	\(7962624\)	\(2.3841\)	\(\Gamma_0(N)\)-optimal