Elliptic curve isogeny class with Cremona label 177870he (LMFDB label 177870.bg)

• Label: 177870he
• Number of curves: $4$
• Conductor: $177870$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 177870he have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177870he do not have complex multiplication.

Modular form 177870.2.a.he

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 177870he

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177870.bg3	177870he1	\([1, 1, 0, -1903332, -773360496]\)	\(3658671062929/880165440\)	\(183446175876881924160\)	\([2]\)	\(9953280\)	\(2.5993\)	\(\Gamma_0(N)\)-optimal
177870.bg4	177870he2	\([1, 1, 0, 4499988, -4854836664]\)	\(48351870250991/76871856600\)	\(-16021815314432303237400\)	\([2]\)	\(19906560\)	\(2.9459\)
177870.bg1	177870he3	\([1, 1, 0, -143843592, -664084101204]\)	\(1579250141304807889/41926500\)	\(8738420918801458500\)	\([2]\)	\(29859840\)	\(3.1486\)
177870.bg2	177870he4	\([1, 1, 0, -143665722, -665808123966]\)	\(-1573398910560073969/8138108343750\)	\(-1696163910426524767593750\)	\([2]\)	\(59719680\)	\(3.4952\)