Cremona's table of elliptic curves

610 = 2 · 5 · 61

Field	Data	Notes
Atkin-Lehner	2+ 5- 61-	Signs for the Atkin-Lehner involutions
Class	610b	Isogeny class
Conductor	610	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-59570312500 = -1 · 22 · 512 · 61	Discriminant
Eigenvalues	2+  0 5-  0 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,976,-732]	[a1,a2,a3,a4,a6]
Generators	[2:34:1]	Generators of the group modulo torsion
j	102759703687719/59570312500	j-invariant
L	1.6222091649525	L(r)(E,1)/r!
Ω	0.65974361263728	Real period
R	1.6392319014835	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	4880g4 19520a4 5490u4 3050j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 610b4

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	-	0	-4	-2	-2	-4	0	-2	0	10	-6	-4	-4	2	-12	-	4	0	2	-8	0	-14	18

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Quadratic twists for elliptic curve 610b4

-4	8	-3	5	-7	-11	13	61
4880g4	19520a4	5490u4	3050j4	29890b3	73810o3	103090k3	37210e3

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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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