Elliptic curve isogeny class with LMFDB label 1568.e (Cremona label 1568g)

• Label: 1568.e
• Number of curves: $4$
• Conductor: $1568$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Rank

The elliptic curves in class 1568.e have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 1568.e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 1568.2.a.e

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 1568.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
1568.e1	1568g2	\([0, 0, 0, -539, -4802]\)	\(287496\)	\(60236288\)	\([2]\)	\(384\)	\(0.35557\)		\(-16\)
1568.e2	1568g3	\([0, 0, 0, -539, 4802]\)	\(287496\)	\(60236288\)	\([2]\)	\(384\)	\(0.35557\)		\(-16\)
1568.e3	1568g1	\([0, 0, 0, -49, 0]\)	\(1728\)	\(7529536\)	\([2, 2]\)	\(192\)	\(0.0089957\)	\(\Gamma_0(N)\)-optimal	\(-4\)
1568.e4	1568g4	\([0, 0, 0, 196, 0]\)	\(1728\)	\(-481890304\)	\([2]\)	\(384\)	\(0.35557\)		\(-4\)