Elliptic curve isogeny class with LMFDB label 20280.l (Cremona label 20280i)

• Label: 20280.l
• Number of curves: $2$
• Conductor: $20280$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 20280.l have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 20280.2.a.l

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.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20280.l1	20280i1	\([0, -1, 0, -95, -300]\)	\(2725888/225\)	\(7909200\)	\([2]\)	\(3840\)	\(0.065965\)	\(\Gamma_0(N)\)-optimal
20280.l2	20280i2	\([0, -1, 0, 100, -1548]\)	\(194672/1875\)	\(-1054560000\)	\([2]\)	\(7680\)	\(0.41254\)