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	710d	Isogeny class
Conductor	710	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	22187500000 = 25 · 510 · 71	Discriminant
Eigenvalues	2- -1 5-  3  2 -1  8 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1105,11727]	[a1,a2,a3,a4,a6]
j	149222774347921/22187500000	j-invariant
L	2.3134875268592	L(r)(E,1)/r!
Ω	1.1567437634296	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	5680h1 22720g1 6390d1 3550d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 710d1

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	-	3	2	-1	8	-5	-1	0	7	-12	12	9	-7	-6	0	2	8	-	-11	10	-16	-15	-2

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Quadratic twists for elliptic curve 710d1

-4	8	-3	5	-7	-11	13	-71
5680h1	22720g1	6390d1	3550d1	34790q1	85910j1	119990a1	50410p1

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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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