Elliptic curve isogeny class with Cremona label 207936ds (LMFDB label 207936.dz)

• Label: 207936ds
• Number of curves: $2$
• Conductor: $207936$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 207936ds 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 207936ds do not have complex multiplication.

Modular form 207936.2.a.ds

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 207936ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
207936.dz1	207936ds1	\([0, 0, 0, -21660, -768208]\)	\(54000/19\)	\(395420253437952\)	\([2]\)	\(368640\)	\(1.5022\)	\(\Gamma_0(N)\)-optimal
207936.dz2	207936ds2	\([0, 0, 0, 64980, -5377456]\)	\(364500/361\)	\(-30051939261284352\)	\([2]\)	\(737280\)	\(1.8488\)