Elliptic curve isogeny class with LMFDB label 246840.be (Cremona label 246840be)

• Label: 246840.be
• Number of curves: $4$
• Conductor: $246840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 246840.be have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 246840.be do not have complex multiplication.

Modular form 246840.2.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 246840.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
246840.be1	246840be3	\([0, -1, 0, -484040, 38059452]\)	\(6913728144004/3658971285\)	\(6637661008512906240\)	\([2]\)	\(4423680\)	\(2.3031\)
246840.be2	246840be2	\([0, -1, 0, -278340, -55986588]\)	\(5258429611216/47403225\)	\(21498292399161600\)	\([2, 2]\)	\(2211840\)	\(1.9565\)
246840.be3	246840be1	\([0, -1, 0, -277735, -56244560]\)	\(83587439220736/6885\)	\(195155159760\)	\([2]\)	\(1105920\)	\(1.6100\)	\(\Gamma_0(N)\)-optimal
246840.be4	246840be4	\([0, -1, 0, -82320, -133532100]\)	\(-34008619684/4228250625\)	\(-7670378399207040000\)	\([2]\)	\(4423680\)	\(2.3031\)