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	5859375000 = 23 · 3 · 512	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-454,-544]	[a1,a2,a3,a4,a6]
j	10316097499609/5859375000	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	240b7 960e8 90c7 150c8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 30a8

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 30a8

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
240b7	960e8	90c7	150c8	1470d7	3630w7	5070v8	8670e8	10830v7	15870u7	25230p8	28830h8	41070bl8	50430f8	55470bc8	66270m8	84270bg8	104430bb8	111630x8

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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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