Elliptic curve isogeny class with Cremona label 207368p (LMFDB label 207368.e)

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

Rank

The elliptic curves in class 207368p 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 207368.2.a.p

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 207368p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
207368.e1	207368p1	\([0, 1, 0, -1149164, -379069664]\)	\(109744/23\)	\(35173628925910356224\)	\([2]\)	\(5677056\)	\(2.4654\)	\(\Gamma_0(N)\)-optimal
207368.e2	207368p2	\([0, 1, 0, 2479776, -2286440528]\)	\(275684/529\)	\(-3235973861183752772608\)	\([2]\)	\(11354112\)	\(2.8120\)