Elliptic curve isogeny class with LMFDB label 7056.y (Cremona label 7056bc)

• Label: 7056.y
• Number of curves: $2$
• Conductor: $7056$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Rank

The elliptic curves in class 7056.y 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 7056.y has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 7056.2.a.y

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 7056.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7056.y1	7056bc1	\([0, 0, 0, 0, -784]\)	\(0\)	\(-265531392\)	\([]\)	\(1728\)	\(0.29532\)	\(\Gamma_0(N)\)-optimal	\(-3\)
7056.y2	7056bc2	\([0, 0, 0, 0, 21168]\)	\(0\)	\(-193572384768\)	\([]\)	\(5184\)	\(0.84463\)		\(-3\)