Elliptic curve isogeny class with Cremona label 60840q (LMFDB label 60840.z)

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

Rank

The elliptic curves in class 60840q 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 60840.2.a.q

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 60840q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
60840.z3	60840q1	\([0, 0, 0, -169338, -26757263]\)	\(9538484224/26325\)	\(1482094872133200\)	\([2]\)	\(516096\)	\(1.7840\)	\(\Gamma_0(N)\)-optimal
60840.z2	60840q2	\([0, 0, 0, -237783, -3088982]\)	\(1650587344/950625\)	\(856321481676960000\)	\([2, 2]\)	\(1032192\)	\(2.1305\)
60840.z4	60840q3	\([0, 0, 0, 948597, -24681098]\)	\(26198797244/15234375\)	\(-54892402671600000000\)	\([2]\)	\(2064384\)	\(2.4771\)
60840.z1	60840q4	\([0, 0, 0, -2519283, 1533273118]\)	\(490757540836/2142075\)	\(7718310954848332800\)	\([2]\)	\(2064384\)	\(2.4771\)