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	610a	Isogeny class
Conductor	610	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-244000 = -1 · 25 · 53 · 61	Discriminant
Eigenvalues	2+  0 5+  0  2  1  7 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-35,-75]	[a1,a2,a3,a4,a6]
j	-4818245769/244000	j-invariant
L	0.97722202165468	L(r)(E,1)/r!
Ω	0.97722202165468	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4880f1 19520i1 5490v1 3050i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 610a1

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	2	1	7	-1	6	1	-3	4	9	-1	11	2	0	-	13	0	-4	7	-6	-2	-12

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Quadratic twists for elliptic curve 610a1

-4	8	-3	5	-7	-11	13	61
4880f1	19520i1	5490v1	3050i1	29890g1	73810i1	103090s1	37210c1

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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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