Elliptic curve isogeny class with Cremona label 60840r (LMFDB label 60840.a)

• Label: 60840r
• Number of curves: $4$
• Conductor: $60840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 60840r have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 60840r do not have complex multiplication.

Modular form 60840.2.a.r

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 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 60840r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60840.a4	60840r1	\([0, 0, 0, 5577, 74698]\)	\(21296/15\)	\(-13511976042240\)	\([2]\)	\(122880\)	\(1.2080\)	\(\Gamma_0(N)\)-optimal
60840.a3	60840r2	\([0, 0, 0, -24843, 628342]\)	\(470596/225\)	\(810718562534400\)	\([2, 2]\)	\(245760\)	\(1.5546\)
60840.a2	60840r3	\([0, 0, 0, -207363, -35912162]\)	\(136835858/1875\)	\(13511976042240000\)	\([2]\)	\(491520\)	\(1.9012\)
60840.a1	60840r4	\([0, 0, 0, -329043, 72602062]\)	\(546718898/405\)	\(2918586825123840\)	\([2]\)	\(491520\)	\(1.9012\)