Elliptic curve isogeny class with Cremona label 56144r (LMFDB label 56144.e)

• Label: 56144r
• Number of curves: $2$
• Conductor: $56144$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 56144r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 56144r do not have complex multiplication.

Modular form 56144.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 56144r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56144.e1	56144r1	\([0, -1, 0, -524, 7372]\)	\(-35152/29\)	\(-13152068864\)	\([]\)	\(43200\)	\(0.63963\)	\(\Gamma_0(N)\)-optimal
56144.e2	56144r2	\([0, -1, 0, 4316, -118468]\)	\(19600688/24389\)	\(-11060889914624\)	\([]\)	\(129600\)	\(1.1889\)