Elliptic curve isogeny class with Cremona label 126960l (LMFDB label 126960.bu)

• Label: 126960l
• Number of curves: $4$
• Conductor: $126960$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 126960l have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.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 126960l do not have complex multiplication.

Modular form 126960.2.a.l

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 Cremona 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 Cremona labels.

Elliptic curves in class 126960l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126960.bu4	126960l1	\([0, -1, 0, 1940, -15968]\)	\(21296/15\)	\(-568457813760\)	\([2]\)	\(180224\)	\(0.94400\)	\(\Gamma_0(N)\)-optimal
126960.bu3	126960l2	\([0, -1, 0, -8640, -126000]\)	\(470596/225\)	\(34107468825600\)	\([2, 2]\)	\(360448\)	\(1.2906\)
126960.bu2	126960l3	\([0, -1, 0, -72120, 7390032]\)	\(136835858/1875\)	\(568457813760000\)	\([2]\)	\(720896\)	\(1.6371\)
126960.bu1	126960l4	\([0, -1, 0, -114440, -14853360]\)	\(546718898/405\)	\(122786887772160\)	\([2]\)	\(720896\)	\(1.6371\)