Elliptic curve isogeny class with LMFDB label 7803.k (Cremona label 7803a)

• Label: 7803.k
• Number of curves: $4$
• Conductor: $7803$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Rank

The elliptic curves in class 7803.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 23 T^{2}\)	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 7803.k has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 7803.2.a.k

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.

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 7803.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7803.k1	7803a4	\([0, 0, 1, -78030, -8390176]\)	\(-12288000\)	\(-4275897935643\)	\([]\)	\(15552\)	\(1.4688\)		\(-27\)
7803.k2	7803a3	\([0, 0, 1, -8670, 310747]\)	\(-12288000\)	\(-5865429267\)	\([]\)	\(5184\)	\(0.91945\)		\(-27\)
7803.k3	7803a2	\([0, 0, 1, 0, -33163]\)	\(0\)	\(-475099770627\)	\([]\)	\(5184\)	\(0.91945\)		\(-3\)
7803.k4	7803a1	\([0, 0, 1, 0, 1228]\)	\(0\)	\(-651714363\)	\([]\)	\(1728\)	\(0.37014\)	\(\Gamma_0(N)\)-optimal	\(-3\)