Elliptic curve isogeny class with Cremona label 7056bs (LMFDB label 7056.bl)

• Label: 7056bs
• Number of curves: $2$
• Conductor: $7056$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7056bs have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7056bs do not have complex multiplication.

Modular form 7056.2.a.bs

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 7056bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7056.bl2	7056bs1	\([0, 0, 0, -147, -1582]\)	\(-2401/6\)	\(-877879296\)	\([]\)	\(2304\)	\(0.40398\)	\(\Gamma_0(N)\)-optimal
7056.bl1	7056bs2	\([0, 0, 0, -20307, 1155602]\)	\(-6329617441/279936\)	\(-40958336434176\)	\([]\)	\(16128\)	\(1.3769\)