Elliptic curve isogeny class with Cremona label 202860cj (LMFDB label 202860.cn)

• Label: 202860cj
• Number of curves: $2$
• Conductor: $202860$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 202860cj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 202860cj do not have complex multiplication.

Modular form 202860.2.a.cj

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 202860cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
202860.cn2	202860cj1	\([0, 0, 0, -31752, -1919771]\)	\(69657034752/8984375\)	\(456625181250000\)	\([2]\)	\(691200\)	\(1.5416\)	\(\Gamma_0(N)\)-optimal
202860.cn1	202860cj2	\([0, 0, 0, -491127, -132474146]\)	\(16110654114672/330625\)	\(268860906720000\)	\([2]\)	\(1382400\)	\(1.8881\)