Elliptic curve isogeny class with Cremona label 219024bf (LMFDB label 219024.bq)

• Label: 219024bf
• Number of curves: $4$
• Conductor: $219024$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 219024bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 219024bf do not have complex multiplication.

Modular form 219024.2.a.bf

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 219024bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
219024.bq3	219024bf1	\([0, 0, 0, -12675, -575614]\)	\(-140625/8\)	\(-12811355062272\)	\([]\)	\(331776\)	\(1.2720\)	\(\Gamma_0(N)\)-optimal
219024.bq4	219024bf2	\([0, 0, 0, 68445, -1067742]\)	\(3375/2\)	\(-21013825140891648\)	\([]\)	\(995328\)	\(1.8213\)
219024.bq2	219024bf3	\([0, 0, 0, -256035, 101294882]\)	\(-1159088625/2097152\)	\(-3358419861444231168\)	\([]\)	\(2322432\)	\(2.2450\)
219024.bq1	219024bf4	\([0, 0, 0, -26214435, 51660561186]\)	\(-189613868625/128\)	\(-1344884809017065472\)	\([]\)	\(6967296\)	\(2.7943\)