Elliptic curve isogeny class with Cremona label 227136jl (LMFDB label 227136.er)

• Label: 227136jl
• Number of curves: $2$
• Conductor: $227136$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 227136jl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 227136jl do not have complex multiplication.

Modular form 227136.2.a.jl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 227136jl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227136.er1	227136jl1	\([0, -1, 0, -344395861, -2459880647147]\)	\(416013434950254592/771895089\)	\(8382014451018013897728\)	\([2]\)	\(57507840\)	\(3.4627\)	\(\Gamma_0(N)\)-optimal
227136.er2	227136jl2	\([0, -1, 0, -340836721, -2513214360047]\)	\(-25203028990703632/1121144263281\)	\(-194792220868704852751368192\)	\([2]\)	\(115015680\)	\(3.8093\)