Elliptic curve isogeny class with Cremona label 36400bs (LMFDB label 36400.cd)

• Label: 36400bs
• Number of curves: $3$
• Conductor: $36400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 36400bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 36400bs do not have complex multiplication.

Modular form 36400.2.a.bs

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 36400bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36400.cd2	36400bs1	\([0, 1, 0, -231379008, -1468984984012]\)	\(-21405018343206000779641/2177246093750000000\)	\(-139343750000000000000000000\)	\([]\)	\(12192768\)	\(3.7564\)	\(\Gamma_0(N)\)-optimal
36400.cd3	36400bs2	\([0, 1, 0, 1424870992, 1347827515988]\)	\(4998853083179567995470359/2905108466204672000000\)	\(-185926941837099008000000000000\)	\([]\)	\(36578304\)	\(4.3057\)
36400.cd1	36400bs3	\([0, 1, 0, -20201279008, 1172022159615988]\)	\(-14245586655234650511684983641/1028175397808386133196800\)	\(-65803225459736712524595200000000\)	\([]\)	\(109734912\)	\(4.8550\)