Elliptic curve isogeny class with Cremona label 218736dl (LMFDB label 218736.fc)

• Label: 218736dl
• Number of curves: $2$
• Conductor: $218736$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 218736dl have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 218736dl do not have complex multiplication.

Modular form 218736.2.a.dl

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 218736dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
218736.fc2	218736dl1	\([0, 0, 0, 36309, 4847962]\)	\(406869021/1015808\)	\(-13216716699992064\)	\([]\)	\(1658880\)	\(1.7772\)	\(\Gamma_0(N)\)-optimal
218736.fc1	218736dl2	\([0, 0, 0, -340011, -163567782]\)	\(-458314011/953312\)	\(-9042208986129629184\)	\([]\)	\(4976640\)	\(2.3265\)