Elliptic curve isogeny class with Cremona label 227136cf (LMFDB label 227136.ji)

• Label: 227136cf
• Number of curves: $2$
• Conductor: $227136$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 227136cf have rank \(0\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 227136.2.a.cf

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 227136cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227136.ji1	227136cf1	\([0, 1, 0, -344395861, 2459880647147]\)	\(416013434950254592/771895089\)	\(8382014451018013897728\)	\([2]\)	\(57507840\)	\(3.4627\)	\(\Gamma_0(N)\)-optimal
227136.ji2	227136cf2	\([0, 1, 0, -340836721, 2513214360047]\)	\(-25203028990703632/1121144263281\)	\(-194792220868704852751368192\)	\([2]\)	\(115015680\)	\(3.8093\)