Elliptic curve isogeny class with LMFDB label 355008.bz (Cremona label 355008bz)

• Label: 355008.bz
• Number of curves: $2$
• Conductor: $355008$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 355008.bz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 355008.bz do not have complex multiplication.

Modular form 355008.2.a.bz

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.

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

Isogeny graph

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

Elliptic curves in class 355008.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355008.bz1	355008bz2	\([0, -1, 0, -5217, -108927]\)	\(3014284/729\)	\(3798506078208\)	\([2]\)	\(878592\)	\(1.1248\)
355008.bz2	355008bz1	\([0, -1, 0, -1777, 27985]\)	\(476656/27\)	\(35171352576\)	\([2]\)	\(439296\)	\(0.77819\)	\(\Gamma_0(N)\)-optimal