Elliptic curve isogeny class with LMFDB label 152880.fd (Cremona label 152880cd)

• Label: 152880.fd
• Number of curves: $4$
• Conductor: $152880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 152880.fd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 152880.fd do not have complex multiplication.

Modular form 152880.2.a.fd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 152880.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
152880.fd1	152880cd4	\([0, 1, 0, -684100776, -6887152094796]\)	\(73474353581350183614361/576510977802240\)	\(277815050352458685480960\)	\([2]\)	\(37324800\)	\(3.6715\)
152880.fd2	152880cd3	\([0, 1, 0, -41847976, -112412659276]\)	\(-16818951115904497561/1592332281446400\)	\(-767329487175219255705600\)	\([2]\)	\(18662400\)	\(3.3249\)
152880.fd3	152880cd2	\([0, 1, 0, -12545976, 639709524]\)	\(453198971846635561/261896250564000\)	\(126205263800746131456000\)	\([2]\)	\(12441600\)	\(3.1222\)
152880.fd4	152880cd1	\([0, 1, 0, 3134024, 81501524]\)	\(7064514799444439/4094064000000\)	\(-1972889745555456000000\)	\([2]\)	\(6220800\)	\(2.7756\)	\(\Gamma_0(N)\)-optimal