Elliptic curve isogeny class with Cremona label 100800nr (LMFDB label 100800.ju)

• Label: 100800nr
• Number of curves: $2$
• Conductor: $100800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 100800nr have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 100800nr do not have complex multiplication.

Modular form 100800.2.a.nr

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 100800nr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.ju2	100800nr1	\([0, 0, 0, 60, -520]\)	\(1280/7\)	\(-130636800\)	\([]\)	\(27648\)	\(0.23939\)	\(\Gamma_0(N)\)-optimal
100800.ju1	100800nr2	\([0, 0, 0, -3540, -81160]\)	\(-262885120/343\)	\(-6401203200\)	\([]\)	\(82944\)	\(0.78870\)