Elliptic curve isogeny class with Cremona label 87120gl (LMFDB label 87120.dj)

• Label: 87120gl
• Number of curves: $4$
• Conductor: $87120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 87120gl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 87120gl do not have complex multiplication.

Modular form 87120.2.a.gl

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 87120gl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87120.dj3	87120gl1	\([0, 0, 0, -45012, -4806241]\)	\(-488095744/200475\)	\(-4142512657364400\)	\([2]\)	\(552960\)	\(1.7050\)	\(\Gamma_0(N)\)-optimal
87120.dj2	87120gl2	\([0, 0, 0, -780087, -265169806]\)	\(158792223184/16335\)	\(5400609094045440\)	\([2]\)	\(1105920\)	\(2.0516\)
87120.dj4	87120gl3	\([0, 0, 0, 347028, 52549211]\)	\(223673040896/187171875\)	\(-3867623700162750000\)	\([2]\)	\(1658880\)	\(2.2543\)
87120.dj1	87120gl4	\([0, 0, 0, -1694847, 461332586]\)	\(1628514404944/664335375\)	\(219639771516442464000\)	\([2]\)	\(3317760\)	\(2.6009\)