Elliptic curve isogeny class with Cremona label 125840ck (LMFDB label 125840.cp)

• Label: 125840ck
• Number of curves: $4$
• Conductor: $125840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 125840ck have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 125840ck do not have complex multiplication.

Modular form 125840.2.a.ck

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 125840ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
125840.cp2	125840ck1	\([0, -1, 0, -62960, 6065600]\)	\(3803721481/26000\)	\(188664160256000\)	\([2]\)	\(622080\)	\(1.5732\)	\(\Gamma_0(N)\)-optimal
125840.cp3	125840ck2	\([0, -1, 0, -24240, 13406912]\)	\(-217081801/10562500\)	\(-76644815104000000\)	\([2]\)	\(1244160\)	\(1.9198\)
125840.cp1	125840ck3	\([0, -1, 0, -401760, -93948160]\)	\(988345570681/44994560\)	\(326494649172623360\)	\([2]\)	\(1866240\)	\(2.1225\)
125840.cp4	125840ck4	\([0, -1, 0, 217760, -358111488]\)	\(157376536199/7722894400\)	\(-56039745643144806400\)	\([2]\)	\(3732480\)	\(2.4691\)