Elliptic curve isogeny class with Cremona label 58800hc (LMFDB label 58800.bf)

• Label: 58800hc
• Number of curves: $2$
• Conductor: $58800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 58800hc have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 58800hc do not have complex multiplication.

Modular form 58800.2.a.hc

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 58800hc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58800.bf1	58800hc1	\([0, -1, 0, -6533, -206163]\)	\(-102400/3\)	\(-903544320000\)	\([]\)	\(79200\)	\(1.0730\)	\(\Gamma_0(N)\)-optimal
58800.bf2	58800hc2	\([0, -1, 0, 32667, 10025037]\)	\(20480/243\)	\(-45741931200000000\)	\([]\)	\(396000\)	\(1.8777\)