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	710a	Isogeny class
Conductor	710	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	355000 = 23 · 54 · 71	Discriminant
Eigenvalues	2+ -1 5-  1 -2 -1 -2 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27,-59]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1]	Generators of the group modulo torsion
j	2305199161/355000	j-invariant
L	1.5321809045201	L(r)(E,1)/r!
Ω	2.105997718189	Real period
R	0.18188302049036	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	5680g1 22720f1 6390p1 3550m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 710a1

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	-2	-7	9	-2	-5	-10	-6	-3	11	-10	-6	6	-14	-	3	-10	-4	-15	-18

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Quadratic twists for elliptic curve 710a1

-4	8	-3	5	-7	-11	13	-71
5680g1	22720f1	6390p1	3550m1	34790d1	85910p1	119990l1	50410g1

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

Part of Computational Number Theory
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