Elliptic curve isogeny class with LMFDB label 369600.fd (Cremona label 369600fd)

• Label: 369600.fd
• Number of curves: $4$
• Conductor: $369600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 369600.fd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 369600.fd do not have complex multiplication.

Modular form 369600.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 369600.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
369600.fd1	369600fd4	\([0, -1, 0, -5174433, -4528735263]\)	\(29925549856274696/4851\)	\(2483712000000\)	\([2]\)	\(5242880\)	\(2.2223\)
369600.fd2	369600fd2	\([0, -1, 0, -323433, -70666263]\)	\(58465284603328/23532201\)	\(1506060864000000\)	\([2, 2]\)	\(2621440\)	\(1.8757\)
369600.fd3	369600fd3	\([0, -1, 0, -274433, -92863263]\)	\(-4464412682696/4706920449\)	\(-2409943269888000000\)	\([2]\)	\(5242880\)	\(2.2223\)
369600.fd4	369600fd1	\([0, -1, 0, -23308, -737138]\)	\(1400416996672/570715299\)	\(570715299000000\)	\([2]\)	\(1310720\)	\(1.5292\)	\(\Gamma_0(N)\)-optimal