Elliptic curve isogeny class with Cremona label 178752df (LMFDB label 178752.s)

• Label: 178752df
• Number of curves: $4$
• Conductor: $178752$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 178752df have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 178752df do not have complex multiplication.

Modular form 178752.2.a.df

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 178752df

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
178752.s3	178752df1	\([0, -1, 0, -26084, -1612806]\)	\(260672203072/399\)	\(3004284864\)	\([2]\)	\(245760\)	\(1.0859\)	\(\Gamma_0(N)\)-optimal
178752.s2	178752df2	\([0, -1, 0, -26329, -1580711]\)	\(4188852928/159201\)	\(76717418287104\)	\([2, 2]\)	\(491520\)	\(1.4325\)
178752.s1	178752df3	\([0, -1, 0, -67489, 4617985]\)	\(8818423496/2736741\)	\(10550471619674112\)	\([2]\)	\(983040\)	\(1.7790\)
178752.s4	178752df4	\([0, -1, 0, 10911, -5729247]\)	\(37259704/3695139\)	\(-14245213248258048\)	\([2]\)	\(983040\)	\(1.7790\)