Elliptic curve isogeny class with Cremona label 7436a (LMFDB label 7436.c)

• Label: 7436a
• Number of curves: $2$
• Conductor: $7436$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7436a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7436a do not have complex multiplication.

Modular form 7436.2.a.a

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 7436a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7436.c2	7436a1	\([0, 1, 0, 15323, -327209]\)	\(321978368/224939\)	\(-277948822950656\)	\([]\)	\(20160\)	\(1.4601\)	\(\Gamma_0(N)\)-optimal
7436.c1	7436a2	\([0, 1, 0, -282117, -59071609]\)	\(-2009615368192/53094899\)	\(-65607407704906496\)	\([]\)	\(60480\)	\(2.0094\)