Cremona's table of elliptic curves

710 = 2 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 5+ 71-	Signs for the Atkin-Lehner involutions
Class	710b	Isogeny class
Conductor	710	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	272	Modular degree for the optimal curve
Δ	232652800 = 217 · 52 · 71	Discriminant
Eigenvalues	2- -1 5+ -1 -2 -1 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-416,3009]	[a1,a2,a3,a4,a6]
Generators	[-11:85:1]	Generators of the group modulo torsion
j	7962857630209/232652800	j-invariant
L	2.4992935439584	L(r)(E,1)/r!
Ω	1.7560060270687	Real period
R	0.041861265002912	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5680f1 22720t1 6390k1 3550c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 710b1

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
-	-1	+	-1	-2	-1	-4	-1	-5	4	-9	-8	8	-7	13	-6	-8	10	4	-	-7	6	-16	17	18

---

Quadratic twists for elliptic curve 710b1

-4	8	-3	5	-7	-11	13	-71
5680f1	22720t1	6390k1	3550c1	34790bb1	85910c1	119990h1	50410j1

---

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