Elliptic curve isogeny class with Cremona label 70070ci (LMFDB label 70070.ck)

• Label: 70070ci
• Number of curves: $4$
• Conductor: $70070$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 70070ci have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 70070ci do not have complex multiplication.

Modular form 70070.2.a.ci

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 70070ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70070.ck4	70070ci1	\([1, 1, 1, 5095, 5095]\)	\(124326214271/71980480\)	\(-8468431491520\)	\([2]\)	\(221184\)	\(1.1701\)	\(\Gamma_0(N)\)-optimal
70070.ck3	70070ci2	\([1, 1, 1, -20385, 15287]\)	\(7962857630209/4606058600\)	\(541898188231400\)	\([2]\)	\(442368\)	\(1.5167\)
70070.ck2	70070ci3	\([1, 1, 1, -70365, 7641647]\)	\(-327495950129089/26547449500\)	\(-3123280886225500\)	\([2]\)	\(663552\)	\(1.7194\)
70070.ck1	70070ci4	\([1, 1, 1, -1146895, 472271995]\)	\(1418098748958579169/8307406250\)	\(977358037906250\)	\([2]\)	\(1327104\)	\(2.0660\)