Elliptic curve isogeny class with LMFDB label 148720.be (Cremona label 148720bu)

• Label: 148720.be
• Number of curves: $4$
• Conductor: $148720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 148720.be have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 148720.be do not have complex multiplication.

Modular form 148720.2.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 148720.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
148720.be1	148720bu3	\([0, 0, 0, -1275443, 28530242]\)	\(46424454082884/26794860125\)	\(132437680133213312000\)	\([2]\)	\(4423680\)	\(2.5506\)
148720.be2	148720bu2	\([0, 0, 0, -852943, -302118258]\)	\(55537159171536/228765625\)	\(282677242276000000\)	\([2, 2]\)	\(2211840\)	\(2.2040\)
148720.be3	148720bu1	\([0, 0, 0, -852098, -302748797]\)	\(885956203616256/15125\)	\(1168087778000\)	\([2]\)	\(1105920\)	\(1.8574\)	\(\Gamma_0(N)\)-optimal
148720.be4	148720bu4	\([0, 0, 0, -443963, -592412262]\)	\(-1957960715364/29541015625\)	\(-146010972250000000000\)	\([2]\)	\(4423680\)	\(2.5506\)