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	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	1952000 = 28 · 53 · 61	Discriminant
Eigenvalues	2+  0 5-  0 -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-164,848]	[a1,a2,a3,a4,a6]
Generators	[-8:44:1]	Generators of the group modulo torsion
j	489490178841/1952000	j-invariant
L	1.6222091649525	L(r)(E,1)/r!
Ω	2.6389744505491	Real period
R	0.40980797537087	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4880g1 19520a1 5490u1 3050j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 610b1

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 610b1

-4	8	-3	5	-7	-11	13	61
4880g1	19520a1	5490u1	3050j1	29890b1	73810o1	103090k1	37210e1

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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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