Elliptic curve isogeny class with Cremona label 176400dj (LMFDB label 176400.ra)

• Label: 176400dj
• Number of curves: $2$
• Conductor: $176400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 176400dj have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 176400dj do not have complex multiplication.

Modular form 176400.2.a.dj

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 176400dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.ra2	176400dj1	\([0, 0, 0, -15435, -3241350]\)	\(-189/2\)	\(-4303400887296000\)	\([]\)	\(774144\)	\(1.6820\)	\(\Gamma_0(N)\)-optimal
176400.ra1	176400dj2	\([0, 0, 0, -48172635, 128691319050]\)	\(-5745702166029/8192\)	\(-17626730034364416000\)	\([]\)	\(10063872\)	\(2.9644\)