Elliptic curve isogeny class with LMFDB label 3249.e (Cremona label 3249a)

• Label: 3249.e
• Number of curves: $2$
• Conductor: $3249$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $0$

Rank

The elliptic curves in class 3249.e have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 3249.e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 3249.2.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.

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 3249.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
3249.e1	3249a2	\([0, 0, 1, -123462, 16713668]\)	\(-884736\)	\(-235239331680891\)	\([]\)	\(12160\)	\(1.6714\)		\(-19\)
3249.e2	3249a1	\([0, 0, 1, -342, -2437]\)	\(-884736\)	\(-5000211\)	\([]\)	\(640\)	\(0.19916\)	\(\Gamma_0(N)\)-optimal	\(-19\)