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

• Label: 36400cd
• Number of curves: $4$
• Conductor: $36400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 36400cd have rank \(0\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 36400.2.a.cd

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 36400cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36400.bn3	36400cd1	\([0, 0, 0, -800075, -251999750]\)	\(884984855328729/83492864000\)	\(5343543296000000000\)	\([2]\)	\(552960\)	\(2.3317\)	\(\Gamma_0(N)\)-optimal
36400.bn2	36400cd2	\([0, 0, 0, -2848075, 1568672250]\)	\(39920686684059609/6492304000000\)	\(415507456000000000000\)	\([2, 2]\)	\(1105920\)	\(2.6783\)
36400.bn4	36400cd3	\([0, 0, 0, 5151925, 8792672250]\)	\(236293804275620391/658593925444000\)	\(-42150011228416000000000\)	\([4]\)	\(2211840\)	\(3.0248\)
36400.bn1	36400cd4	\([0, 0, 0, -43616075, 110867680250]\)	\(143378317900125424089/4976562500000\)	\(318500000000000000000\)	\([2]\)	\(2211840\)	\(3.0248\)