Elliptic curve isogeny class with LMFDB label 46800.fd (Cremona label 46800dk)

• Label: 46800.fd
• Number of curves: $4$
• Conductor: $46800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 46800.fd have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 46800.fd do not have complex multiplication.

Modular form 46800.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 46800.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46800.fd1	46800dk4	\([0, 0, 0, -74662275, 248313253250]\)	\(986551739719628473/111045168\)	\(5180923358208000000\)	\([2]\)	\(3932160\)	\(3.0153\)
46800.fd2	46800dk3	\([0, 0, 0, -8422275, -3190810750]\)	\(1416134368422073/725251155408\)	\(33837317906715648000000\)	\([2]\)	\(3932160\)	\(3.0153\)
46800.fd3	46800dk2	\([0, 0, 0, -4678275, 3859141250]\)	\(242702053576633/2554695936\)	\(119191893590016000000\)	\([2, 2]\)	\(1966080\)	\(2.6687\)
46800.fd4	46800dk1	\([0, 0, 0, -70275, 149701250]\)	\(-822656953/207028224\)	\(-9659108818944000000\)	\([2]\)	\(983040\)	\(2.3221\)	\(\Gamma_0(N)\)-optimal