Elliptic curve isogeny class with LMFDB label 20280.bf (Cremona label 20280be)

• Label: 20280.bf
• Number of curves: $4$
• Conductor: $20280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 20280.bf have rank \(0\).

L-function data

Bad L-factors:

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

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
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20280.bf do not have complex multiplication.

Modular form 20280.2.a.bf

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 20280.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20280.bf1	20280be3	\([0, 1, 0, -279920, -56881200]\)	\(490757540836/2142075\)	\(10587532174003200\)	\([2]\)	\(258048\)	\(1.9278\)
20280.bf2	20280be2	\([0, 1, 0, -26420, 105600]\)	\(1650587344/950625\)	\(1174652238240000\)	\([2, 2]\)	\(129024\)	\(1.5812\)
20280.bf3	20280be1	\([0, 1, 0, -18815, 984738]\)	\(9538484224/26325\)	\(2033051950800\)	\([4]\)	\(64512\)	\(1.2346\)	\(\Gamma_0(N)\)-optimal
20280.bf4	20280be4	\([0, 1, 0, 105400, 949248]\)	\(26198797244/15234375\)	\(-75298220400000000\)	\([2]\)	\(258048\)	\(1.9278\)