Elliptic curve isogeny class with Cremona label 46800cr (LMFDB label 46800.bt)

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

Rank

The elliptic curves in class 46800cr 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 46800.2.a.cr

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 46800cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
46800.bt1	46800cr1	\([0, 0, 0, -17475, -889150]\)	\(-8538302475/26\)	\(-1797120000\)	\([]\)	\(62208\)	\(1.0030\)	\(\Gamma_0(N)\)-optimal
46800.bt2	46800cr2	\([0, 0, 0, -11475, -1507950]\)	\(-3316275/17576\)	\(-885627924480000\)	\([]\)	\(186624\)	\(1.5523\)