Cremona's table of elliptic curves

10080 = 2⁵ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	10080w	Isogeny class
Conductor	10080	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	115736040000 = 26 · 310 · 54 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1497,15136]	[a1,a2,a3,a4,a6]
Generators	[-13:180:1]	Generators of the group modulo torsion
j	7952095936/2480625	j-invariant
L	4.7530983943812	L(r)(E,1)/r!
Ω	0.97269586358552	Real period
R	1.2216301549953	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10080z1 20160dq2 3360s1 50400do1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080w1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	-	+	0	2	6	-4	-8	2	-8	-2	6	0	0	-6	4	-6	-8	0	-14	8	4	-2	-14

---

Quadratic twists for elliptic curve 10080w1

-4	8	-3	5	-7
10080z1	20160dq2	3360s1	50400do1	70560u1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations