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

• Label: 355008ce
• Number of curves: $2$
• Conductor: $355008$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 355008ce have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 355008.2.a.ce

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 355008ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355008.ce2	355008ce1	\([0, -1, 0, -157211841, 759107264193]\)	\(-140246460241/73728\)	\(-225901970736274873516032\)	\([]\)	\(108186624\)	\(3.4315\)	\(\Gamma_0(N)\)-optimal
355008.ce1	355008ce2	\([0, -1, 0, -9672609601, -412459354507967]\)	\(-32663831300214001/5083731656658\)	\(-15576510958298471391538042109952\)	\([]\)	\(1406426112\)	\(4.7140\)