Elliptic curve isogeny class with Cremona label 63504bg (LMFDB label 63504.bo)

• Label: 63504bg
• Number of curves: $4$
• Conductor: $63504$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 63504bg have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 63504bg do not have complex multiplication.

Modular form 63504.2.a.bg

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 63504bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63504.bo3	63504bg1	\([0, 0, 0, -3675, 89866]\)	\(-140625/8\)	\(-312264916992\)	\([]\)	\(51840\)	\(0.96251\)	\(\Gamma_0(N)\)-optimal
63504.bo4	63504bg2	\([0, 0, 0, 19845, 166698]\)	\(3375/2\)	\(-512192530096128\)	\([]\)	\(155520\)	\(1.5118\)
63504.bo2	63504bg3	\([0, 0, 0, -74235, -15814358]\)	\(-1159088625/2097152\)	\(-81858374399950848\)	\([]\)	\(362880\)	\(1.9355\)
63504.bo1	63504bg4	\([0, 0, 0, -7600635, -8065349334]\)	\(-189613868625/128\)	\(-32780321926152192\)	\([]\)	\(1088640\)	\(2.4848\)