Elliptic curve isogeny class with LMFDB label 338130.cr (Cremona label 338130cr)

• Label: 338130.cr
• Number of curves: $4$
• Conductor: $338130$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 338130.cr have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(13\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 338130.cr do not have complex multiplication.

Modular form 338130.2.a.cr

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 338130.cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
338130.cr1	338130cr3	\([1, -1, 1, -1257638, 543069947]\)	\(12501706118329/2570490\)	\(45231081829592490\)	\([2]\)	\(4718592\)	\(2.1929\)
338130.cr2	338130cr2	\([1, -1, 1, -87188, 6535667]\)	\(4165509529/1368900\)	\(24087558370788900\)	\([2, 2]\)	\(2359296\)	\(1.8464\)
338130.cr3	338130cr1	\([1, -1, 1, -35168, -2453389]\)	\(273359449/9360\)	\(164701253817360\)	\([2]\)	\(1179648\)	\(1.4998\)	\(\Gamma_0(N)\)-optimal
338130.cr4	338130cr4	\([1, -1, 1, 250942, 44676731]\)	\(99317171591/106616250\)	\(-1876050219263366250\)	\([2]\)	\(4718592\)	\(2.1929\)