Elliptic curve isogeny class with Cremona label 59976s (LMFDB label 59976.i)

• Label: 59976s
• Number of curves: $4$
• Conductor: $59976$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 59976s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 59976s do not have complex multiplication.

Modular form 59976.2.a.s

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 59976s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
59976.i4	59976s1	\([0, 0, 0, -311630151, 2137094698970]\)	\(-152435594466395827792/1646846627220711\)	\(-36158373657255268692999936\)	\([2]\)	\(13271040\)	\(3.7201\)	\(\Gamma_0(N)\)-optimal
59976.i3	59976s2	\([0, 0, 0, -4998939771, 136039468613510]\)	\(157304700372188331121828/18069292138401\)	\(1586926690228683686421504\)	\([2, 2]\)	\(26542080\)	\(4.0667\)
59976.i2	59976s3	\([0, 0, 0, -5011799331, 135304372441406]\)	\(79260902459030376659234/842751810121431609\)	\(148028526018239955088831875072\)	\([2]\)	\(53084160\)	\(4.4133\)
59976.i1	59976s4	\([0, 0, 0, -79983034131, 8706526495316174]\)	\(322159999717985454060440834/4250799\)	\(746648660747630592\)	\([2]\)	\(53084160\)	\(4.4133\)