Elliptic curve isogeny class with LMFDB label 159120.cl (Cremona label 159120b)

• Label: 159120.cl
• Number of curves: $4$
• Conductor: $159120$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 159120.cl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 159120.cl do not have complex multiplication.

Modular form 159120.2.a.cl

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 159120.cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159120.cl1	159120b3	\([0, 0, 0, -3759920427, 88734894398746]\)	\(1968666709544018637994033129/113621848881699526875\)	\(339273022811172680056320000\)	\([4]\)	\(122683392\)	\(4.1540\)
159120.cl2	159120b4	\([0, 0, 0, -1237220427, -15664684941254]\)	\(70141892778055497175333129/5090453819946781723125\)	\(15200013659099971076743680000\)	\([2]\)	\(122683392\)	\(4.1540\)
159120.cl3	159120b2	\([0, 0, 0, -248570427, 1217304728746]\)	\(568832774079017834683129/114800389711906640625\)	\(342792126873517838400000000\)	\([2, 2]\)	\(61341696\)	\(3.8075\)
159120.cl4	159120b1	\([0, 0, 0, 32679573, 113623478746]\)	\(1292603583867446566871/2615843353271484375\)	\(-7810866399375000000000000\)	\([2]\)	\(30670848\)	\(3.4609\)	\(\Gamma_0(N)\)-optimal