Elliptic curve isogeny class with Cremona label 3136d (LMFDB label 3136.n)

• Label: 3136d
• Number of curves: $4$
• Conductor: $3136$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Rank

The elliptic curves in class 3136d have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 3136d has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 3136.2.a.d

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 3136d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
3136.n4	3136d1	\([0, 0, 0, -140, -784]\)	\(-3375\)	\(-89915392\)	\([2]\)	\(512\)	\(0.24058\)	\(\Gamma_0(N)\)-optimal	\(-7\)
3136.n3	3136d2	\([0, 0, 0, -2380, -44688]\)	\(16581375\)	\(89915392\)	\([2]\)	\(1024\)	\(0.58716\)		\(-28\)
3136.n2	3136d3	\([0, 0, 0, -6860, 268912]\)	\(-3375\)	\(-10578455953408\)	\([2]\)	\(3584\)	\(1.2135\)		\(-7\)
3136.n1	3136d4	\([0, 0, 0, -116620, 15327984]\)	\(16581375\)	\(10578455953408\)	\([2]\)	\(7168\)	\(1.5601\)		\(-28\)