Elliptic curve isogeny class with Cremona label 79800bu (LMFDB label 79800.bm)

• Label: 79800bu
• Number of curves: $4$
• Conductor: $79800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 79800bu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 79800bu do not have complex multiplication.

Modular form 79800.2.a.bu

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 79800bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
79800.bm4	79800bu1	\([0, 1, 0, -108983, -5460462]\)	\(572616640141312/280535480757\)	\(70133870189250000\)	\([2]\)	\(786432\)	\(1.9257\)	\(\Gamma_0(N)\)-optimal
79800.bm2	79800bu2	\([0, 1, 0, -929108, 340632288]\)	\(22174957026242512/278654127129\)	\(1114616508516000000\)	\([2, 2]\)	\(1572864\)	\(2.2723\)
79800.bm3	79800bu3	\([0, 1, 0, -159608, 888516288]\)	\(-28104147578308/21301741002339\)	\(-340827856037424000000\)	\([2]\)	\(3145728\)	\(2.6189\)
79800.bm1	79800bu4	\([0, 1, 0, -14820608, 21955806288]\)	\(22501000029889239268/3620708343\)	\(57931333488000000\)	\([2]\)	\(3145728\)	\(2.6189\)