Elliptic curve isogeny class with Cremona label 46800by (LMFDB label 46800.bx)

• Label: 46800by
• Number of curves: $2$
• Conductor: $46800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 46800by have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 7 T + 29 T^{2}\)	1.29.ah
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 46800.2.a.by

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 46800by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46800.bx2	46800by1	\([0, 0, 0, 4800, 166000]\)	\(7077888/10985\)	\(-18982080000000\)	\([]\)	\(82944\)	\(1.2332\)	\(\Gamma_0(N)\)-optimal
46800.bx1	46800by2	\([0, 0, 0, -151200, 22734000]\)	\(-303464448/1625\)	\(-2047032000000000\)	\([]\)	\(248832\)	\(1.7825\)