Elliptic curve isogeny class with LMFDB label 784.f (Cremona label 784h)

• Label: 784.f
• Number of curves: $4$
• Conductor: $784$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $1$

Elliptic curves in class 784.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
784.f1	784h4	\([0, 0, 0, -29155, -1915998]\)	\(16581375\)	\(165288374272\)	\([2]\)	\(896\)	\(1.2135\)		\(-28\)
784.f2	784h3	\([0, 0, 0, -1715, -33614]\)	\(-3375\)	\(-165288374272\)	\([2]\)	\(448\)	\(0.86696\)		\(-7\)
784.f3	784h2	\([0, 0, 0, -595, 5586]\)	\(16581375\)	\(1404928\)	\([2]\)	\(128\)	\(0.24058\)		\(-28\)
784.f4	784h1	\([0, 0, 0, -35, 98]\)	\(-3375\)	\(-1404928\)	\([2]\)	\(64\)	\(-0.10599\)	\(\Gamma_0(N)\)-optimal	\(-7\)

Rank

The elliptic curves in class 784.f 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
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 784.f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 784.2.a.f

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.