Elliptic curve isogeny class with LMFDB label 1296.l (Cremona label 1296h)

• Label: 1296.l
• Number of curves: $2$
• Conductor: $1296$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1296.l have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1296.l do not have complex multiplication.

Modular form 1296.2.a.l

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 1296.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1296.l1	1296h2	\([0, 0, 0, -891, 11178]\)	\(-35937/4\)	\(-8707129344\)	\([]\)	\(864\)	\(0.64465\)
1296.l2	1296h1	\([0, 0, 0, 69, -22]\)	\(109503/64\)	\(-21233664\)	\([]\)	\(288\)	\(0.095341\)	\(\Gamma_0(N)\)-optimal