Elliptic curve isogeny class with Cremona label 10816bb (LMFDB label 10816.r)

• Label: 10816bb
• Number of curves: $4$
• Conductor: $10816$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Rank

The elliptic curves in class 10816bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 10816bb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 10816.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 10816bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
10816.r4	10816bb1	\([0, 0, 0, 169, 0]\)	\(1728\)	\(-308915776\)	\([2]\)	\(1920\)	\(0.31852\)	\(\Gamma_0(N)\)-optimal	\(-4\)
10816.r3	10816bb2	\([0, 0, 0, -676, 0]\)	\(1728\)	\(19770609664\)	\([2, 2]\)	\(3840\)	\(0.66509\)		\(-4\)
10816.r1	10816bb3	\([0, 0, 0, -7436, -246064]\)	\(287496\)	\(158164877312\)	\([2]\)	\(7680\)	\(1.0117\)		\(-16\)
10816.r2	10816bb4	\([0, 0, 0, -7436, 246064]\)	\(287496\)	\(158164877312\)	\([2]\)	\(7680\)	\(1.0117\)		\(-16\)