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

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

Rank

The elliptic curves in class 355008.z 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 355008.2.a.z

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

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.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355008.z1	355008z2	\([0, -1, 0, -302433, 64201185]\)	\(-6311547390625/9565938\)	\(-4636650861232128\)	\([]\)	\(3161088\)	\(1.9062\)
355008.z2	355008z1	\([0, -1, 0, 287, -35999]\)	\(5375/1152\)	\(-558379302912\)	\([]\)	\(451584\)	\(0.93324\)	\(\Gamma_0(N)\)-optimal