Elliptic curve isogeny class with LMFDB label 124722.be (Cremona label 124722bv)

• Label: 124722.be
• Number of curves: $4$
• Conductor: $124722$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 124722.be have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(13\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 124722.be do not have complex multiplication.

Modular form 124722.2.a.be

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 124722.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
124722.be1	124722bv4	\([1, -1, 1, -667751, 210180845]\)	\(9357915116017/538002\)	\(1893091180905522\)	\([2]\)	\(1769472\)	\(1.9949\)
124722.be2	124722bv2	\([1, -1, 1, -44141, 2892881]\)	\(2703045457/544644\)	\(1916462676966084\)	\([2, 2]\)	\(884736\)	\(1.6483\)
124722.be3	124722bv1	\([1, -1, 1, -13721, -574999]\)	\(81182737/5904\)	\(20774663164944\)	\([2]\)	\(442368\)	\(1.3018\)	\(\Gamma_0(N)\)-optimal
124722.be4	124722bv3	\([1, -1, 1, 92749, 17184197]\)	\(25076571983/50863698\)	\(-178976319998888178\)	\([2]\)	\(1769472\)	\(1.9949\)