Elliptic curve isogeny class with LMFDB label 1152.l (Cremona label 1152e)

• Label: 1152.l
• Number of curves: $2$
• Conductor: $1152$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1152.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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1152.l do not have complex multiplication.

Modular form 1152.2.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.

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

Isogeny graph

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

Elliptic curves in class 1152.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1152.l1	1152e2	\([0, 0, 0, -120, 416]\)	\(16000/3\)	\(35831808\)	\([2]\)	\(256\)	\(0.16743\)
1152.l2	1152e1	\([0, 0, 0, 15, 38]\)	\(4000/9\)	\(-839808\)	\([2]\)	\(128\)	\(-0.17914\)	\(\Gamma_0(N)\)-optimal