Elliptic curve isogeny class with Cremona label 217800cx (LMFDB label 217800.s)

• Label: 217800cx
• Number of curves: $2$
• Conductor: $217800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 217800cx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 217800cx do not have complex multiplication.

Modular form 217800.2.a.cx

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 217800cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
217800.s2	217800cx1	\([0, 0, 0, -45375, -8318750]\)	\(-432\)	\(-23916073500000000\)	\([2]\)	\(1638400\)	\(1.8312\)	\(\Gamma_0(N)\)-optimal
217800.s1	217800cx2	\([0, 0, 0, -952875, -357706250]\)	\(1000188\)	\(95664294000000000\)	\([2]\)	\(3276800\)	\(2.1777\)