Elliptic curve isogeny class with Cremona label 207936v (LMFDB label 207936.cm)

• Label: 207936v
• Number of curves: $2$
• Conductor: $207936$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $1$

Rank

The elliptic curves in class 207936v have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 207936v has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 207936.2.a.v

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 207936v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
207936.cm2	207936v1	\([0, 0, 0, -1368, 19494]\)	\(-884736\)	\(-320013504\)	\([]\)	\(92160\)	\(0.54573\)	\(\Gamma_0(N)\)-optimal	\(-19\)
207936.cm1	207936v2	\([0, 0, 0, -493848, -133709346]\)	\(-884736\)	\(-15055317227577024\)	\([]\)	\(1751040\)	\(2.0180\)		\(-19\)