Elliptic curve isogeny class with Cremona label 141570ep (LMFDB label 141570.bh)

• Label: 141570ep
• Number of curves: $4$
• Conductor: $141570$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 141570ep have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 141570ep do not have complex multiplication.

Modular form 141570.2.a.ep

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 141570ep

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
141570.bh2	141570ep1	\([1, -1, 0, -35415, 2558925]\)	\(3803721481/26000\)	\(33578167194000\)	\([2]\)	\(622080\)	\(1.4294\)	\(\Gamma_0(N)\)-optimal
141570.bh3	141570ep2	\([1, -1, 0, -13635, 5656041]\)	\(-217081801/10562500\)	\(-13641130422562500\)	\([2]\)	\(1244160\)	\(1.7760\)
141570.bh1	141570ep3	\([1, -1, 0, -225990, -39634380]\)	\(988345570681/44994560\)	\(58109033019248640\)	\([2]\)	\(1866240\)	\(1.9787\)
141570.bh4	141570ep4	\([1, -1, 0, 122490, -151078284]\)	\(157376536199/7722894400\)	\(-9973870745569473600\)	\([2]\)	\(3732480\)	\(2.3253\)