Elliptic curve isogeny class with Cremona label 227520ec (LMFDB label 227520.be)

• Label: 227520ec
• Number of curves: $2$
• Conductor: $227520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 227520ec have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 227520ec do not have complex multiplication.

Modular form 227520.2.a.ec

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 227520ec

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227520.be1	227520ec1	\([0, 0, 0, -723, 2828]\)	\(895841344/444375\)	\(20732760000\)	\([2]\)	\(147456\)	\(0.67259\)	\(\Gamma_0(N)\)-optimal
227520.be2	227520ec2	\([0, 0, 0, 2652, 21728]\)	\(690807104/468075\)	\(-1397664460800\)	\([2]\)	\(294912\)	\(1.0192\)