Elliptic curve isogeny class with Cremona label 207368z (LMFDB label 207368.r)

• Label: 207368z
• Number of curves: $2$
• Conductor: $207368$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 207368z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 207368z do not have complex multiplication.

Modular form 207368.2.a.z

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 207368z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
207368.r2	207368z1	\([0, 0, 0, -1529339, 826309638]\)	\(-22180932/3703\)	\(-66040282881301076992\)	\([2]\)	\(3244032\)	\(2.5301\)	\(\Gamma_0(N)\)-optimal
207368.r1	207368z2	\([0, 0, 0, -25376659, 49202982990]\)	\(50668941906/1127\)	\(40198433058183264256\)	\([2]\)	\(6488064\)	\(2.8766\)