Cremona's table of elliptic curves

30 = 2 · 3 · 5

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+	Signs for the Atkin-Lehner involutions
Class	30a	Isogeny class
Conductor	30	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-1536000 = -1 · 212 · 3 · 53	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-14,-64]	[a1,a2,a3,a4,a6]
j	-273359449/1536000	j-invariant
L	0.55865804320692	L(r)(E,1)/r!
Ω	1.1173160864138	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	240b3 960e3 90c3 150c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 30a3

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

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Quadratic twists for elliptic curve 30a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
240b3	960e3	90c3	150c3	1470d3	3630w3	5070v3	8670e3	10830v3	15870u3	25230p3	28830h3	41070bl3	50430f3	55470bc3	66270m3	84270bg3	104430bb3	111630x3

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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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