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	420b	Isogeny class
Conductor	420	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	680400 = 24 · 35 · 52 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7- -2  4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-565,5362]	[a1,a2,a3,a4,a6]
j	1248870793216/42525	j-invariant
L	1.3397581666493	L(r)(E,1)/r!
Ω	2.6795163332987	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	1680s1 6720t1 1260f1 2100k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 420b1

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

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Quadratic twists for elliptic curve 420b1

-4	8	-3	5	-7	-11	13	17
1680s1	6720t1	1260f1	2100k1	2940i1	50820i1	70980a1	121380u1

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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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