Elliptic curve isogeny class with Cremona label 24640o (LMFDB label 24640.bp)

• Label: 24640o
• Number of curves: $4$
• Conductor: $24640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 24640o have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 24640o do not have complex multiplication.

Modular form 24640.2.a.o

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 24640o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24640.bp4	24640o1	\([0, -1, 0, 639, 50561]\)	\(109902239/4312000\)	\(-1130364928000\)	\([2]\)	\(36864\)	\(0.99266\)	\(\Gamma_0(N)\)-optimal
24640.bp2	24640o2	\([0, -1, 0, -17281, 842625]\)	\(2177286259681/105875000\)	\(27754496000000\)	\([2]\)	\(73728\)	\(1.3392\)
24640.bp3	24640o3	\([0, -1, 0, -5761, -1386879]\)	\(-80677568161/3131816380\)	\(-820986873118720\)	\([2]\)	\(110592\)	\(1.5420\)
24640.bp1	24640o4	\([0, -1, 0, -225281, -40856575]\)	\(4823468134087681/30382271150\)	\(7964530088345600\)	\([2]\)	\(221184\)	\(1.8885\)