Cremona's table of elliptic curves

10710 = 2 · 3² · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	10710bg	Isogeny class
Conductor	10710	Conductor
∏ cp	1728	Product of Tamagawa factors cp
Δ	-4637360159037849600 = -1 · 224 · 38 · 52 · 73 · 173	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 -4 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,131647,-101996719]	[a1,a2,a3,a4,a6]
Generators	[393:3016:1]	Generators of the group modulo torsion
j	346124368852751159/6361262220902400	j-invariant
L	6.478283689852	L(r)(E,1)/r!
Ω	0.1189848698835	Real period
R	1.1342975259857	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	85680dy3 3570n3 53550u3 74970di3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710bg3

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	-4	-	2	-6	0	-4	8	6	-4	-6	-6	-12	14	-4	0	14	-10	-6	-12	2

---

Quadratic twists for elliptic curve 10710bg3

-4	-3	5	-7
85680dy3	3570n3	53550u3	74970di3

---

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