Cremona's table of elliptic curves

420 = 2² · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	420a	Isogeny class
Conductor	420	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-187492384800000 = -1 · 28 · 314 · 55 · 72	Discriminant
Eigenvalues	2- 3+ 5+ 7+  2  4  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11564,448840]	[a1,a2,a3,a4,a6]
j	667990736021936/732392128125	j-invariant
L	1.1310272070445	L(r)(E,1)/r!
Ω	0.37700906901483	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	1680q2 6720x2 1260h2 2100m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 420a2

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	4	6	6	-8	-2	10	2	10	-4	-8	4	-8	6	12	-6	-12	-8	-4	-10	8

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Quadratic twists for elliptic curve 420a2

-4	8	-3	5	-7	-11	13	17
1680q2	6720x2	1260h2	2100m2	2940j2	50820d2	70980o2	121380bg2

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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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