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	610c	Isogeny class
Conductor	610	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-372100 = -1 · 22 · 52 · 612	Discriminant
Eigenvalues	2-  2 5-  0 -6  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,15,-13]	[a1,a2,a3,a4,a6]
j	371694959/372100	j-invariant
L	3.2804783161188	L(r)(E,1)/r!
Ω	1.6402391580594	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4880h2 19520d2 5490f2 3050a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 610c2

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

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Quadratic twists for elliptic curve 610c2

-4	8	-3	5	-7	-11	13	61
4880h2	19520d2	5490f2	3050a2	29890r2	73810f2	103090c2	37210b2

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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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