Elliptic curve isogeny class with LMFDB label 134862.bw (Cremona label 134862n)

• Label: 134862.bw
• Number of curves: $4$
• Conductor: $134862$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 134862.bw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 134862.bw do not have complex multiplication.

Modular form 134862.2.a.bw

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 134862.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
134862.bw1	134862n3	\([1, 0, 0, -3067607, 2067729663]\)	\(661397832743623417/443352042\)	\(2139975626493978\)	\([2]\)	\(2949120\)	\(2.2578\)
134862.bw2	134862n2	\([1, 0, 0, -192917, 31874205]\)	\(164503536215257/4178071044\)	\(20166750917818596\)	\([2, 2]\)	\(1474560\)	\(1.9112\)
134862.bw3	134862n1	\([1, 0, 0, -27297, -1017927]\)	\(466025146777/177366672\)	\(856115048709648\)	\([2]\)	\(737280\)	\(1.5646\)	\(\Gamma_0(N)\)-optimal
134862.bw4	134862n4	\([1, 0, 0, 31853, 101777675]\)	\(740480746823/927484650666\)	\(-4476791259196504794\)	\([2]\)	\(2949120\)	\(2.2578\)