Elliptic curve isogeny class with Cremona label 104040co (LMFDB label 104040.cl)

• Label: 104040co
• Number of curves: $4$
• Conductor: $104040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 104040co have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 104040co do not have complex multiplication.

Modular form 104040.2.a.co

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 104040co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
104040.cl3	104040co1	\([0, 0, 0, -5970162, -5614709051]\)	\(83587439220736/6885\)	\(1938407064158160\)	\([2]\)	\(1769472\)	\(2.3769\)	\(\Gamma_0(N)\)-optimal
104040.cl2	104040co2	\([0, 0, 0, -5983167, -5589018974]\)	\(5258429611216/47403225\)	\(213534922187662905600\)	\([2, 2]\)	\(3538944\)	\(2.7235\)
104040.cl4	104040co3	\([0, 0, 0, -1769547, -13310898986]\)	\(-34008619684/4228250625\)	\(-76187151249672320640000\)	\([2]\)	\(7077888\)	\(3.0701\)
104040.cl1	104040co4	\([0, 0, 0, -10404867, 3777025966]\)	\(6913728144004/3658971285\)	\(65929535269329709347840\)	\([2]\)	\(7077888\)	\(3.0701\)