Elliptic curve isogeny class with LMFDB label 7220.c (Cremona label 7220g)

• Label: 7220.c
• Number of curves: $2$
• Conductor: $7220$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7220.c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7220.c do not have complex multiplication.

Modular form 7220.2.a.c

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 7220.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7220.c1	7220g2	\([0, 1, 0, -180620, -29589980]\)	\(7888624/5\)	\(413040253157120\)	\([2]\)	\(36480\)	\(1.7457\)
7220.c2	7220g1	\([0, 1, 0, -9145, -645000]\)	\(-16384/25\)	\(-129075079111600\)	\([2]\)	\(18240\)	\(1.3992\)	\(\Gamma_0(N)\)-optimal