Elliptic curve isogeny class with LMFDB label 20280.u (Cremona label 20280z)

• Label: 20280.u
• Number of curves: $2$
• Conductor: $20280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 20280.u 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 20280.2.a.u

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 20280.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20280.u1	20280z1	\([0, 1, 0, -27096, 1338624]\)	\(202612/45\)	\(488655331107840\)	\([2]\)	\(89856\)	\(1.5318\)	\(\Gamma_0(N)\)-optimal
20280.u2	20280z2	\([0, 1, 0, 60784, 8298720]\)	\(1143574/2025\)	\(-43978979799705600\)	\([2]\)	\(179712\)	\(1.8784\)