Cremona's table of elliptic curves

3420 = 2² · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 19+	Signs for the Atkin-Lehner involutions
Class	3420b	Isogeny class
Conductor	3420	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7180358400 = 28 · 310 · 52 · 19	Discriminant
Eigenvalues	2- 3- 5- -2  0 -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1047,-12386]	[a1,a2,a3,a4,a6]
j	680136784/38475	j-invariant
L	1.6845068057328	L(r)(E,1)/r!
Ω	0.84225340286639	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	13680bt2 54720bi2 1140b2 17100p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3420b2

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	0	-4	2	+	6	2	0	-4	-2	2	6	12	4	6	12	0	-2	0	6	14	8

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Quadratic twists for elliptic curve 3420b2

-4	8	-3	5	-19
13680bt2	54720bi2	1140b2	17100p2	64980bn2

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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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