Elliptic curve isogeny class with Cremona label 202800bt (LMFDB label 202800.gn)

• Label: 202800bt
• Number of curves: $2$
• Conductor: $202800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 202800bt have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 202800bt do not have complex multiplication.

Modular form 202800.2.a.bt

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 202800bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
202800.gn1	202800bt1	\([0, 1, 0, -57360008, -167640720012]\)	\(-2365581049/6750\)	\(-59554868478768000000000\)	\([]\)	\(22643712\)	\(3.2417\)	\(\Gamma_0(N)\)-optimal
202800.gn2	202800bt2	\([0, 1, 0, 114005992, -858931164012]\)	\(18573478391/46875000\)	\(-413575475547000000000000000\)	\([]\)	\(67931136\)	\(3.7910\)