Elliptic curve isogeny class with Cremona label 61504bm (LMFDB label 61504.be)

• Label: 61504bm
• Number of curves: $4$
• Conductor: $61504$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 61504bm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(31\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 61504bm do not have complex multiplication.

Modular form 61504.2.a.bm

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 61504bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61504.be4	61504bm1	\([0, 0, 0, -42284, 16682960]\)	\(-35937/496\)	\(-115396267416223744\)	\([2]\)	\(368640\)	\(1.9555\)	\(\Gamma_0(N)\)-optimal
61504.be3	61504bm2	\([0, 0, 0, -1272364, 550537680]\)	\(979146657/3844\)	\(894321072475734016\)	\([2, 2]\)	\(737280\)	\(2.3021\)
61504.be2	61504bm3	\([0, 0, 0, -1887404, -36702512]\)	\(3196010817/1847042\)	\(429721275324590194688\)	\([2]\)	\(1474560\)	\(2.6486\)
61504.be1	61504bm4	\([0, 0, 0, -20338604, 35304479952]\)	\(3999236143617/62\)	\(14424533427027968\)	\([2]\)	\(1474560\)	\(2.6486\)