Elliptic curve isogeny class with Cremona label 35280et (LMFDB label 35280.c)

• Label: 35280et
• Number of curves: $2$
• Conductor: $35280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 35280et have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35280et do not have complex multiplication.

Modular form 35280.2.a.et

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 35280et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35280.c2	35280et1	\([0, 0, 0, -5628, 158123]\)	\(4927700992/151875\)	\(607614210000\)	\([2]\)	\(61440\)	\(1.0367\)	\(\Gamma_0(N)\)-optimal
35280.c1	35280et2	\([0, 0, 0, -13503, -382102]\)	\(4253563312/1476225\)	\(94496161939200\)	\([2]\)	\(122880\)	\(1.3833\)