Elliptic curve isogeny class with Cremona label 100800hk (LMFDB label 100800.lo)

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

Rank

The elliptic curves in class 100800hk have rank \(2\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 100800.2.a.hk

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 100800hk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
100800.lo1	100800hk1	\([0, 0, 0, -2880, 59400]\)	\(28311552/49\)	\(4572288000\)	\([2]\)	\(73728\)	\(0.74755\)	\(\Gamma_0(N)\)-optimal
100800.lo2	100800hk2	\([0, 0, 0, -1980, 97200]\)	\(-574992/2401\)	\(-3584673792000\)	\([2]\)	\(147456\)	\(1.0941\)