Cremona's table of elliptic curves

620 = 2² · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 31+	Signs for the Atkin-Lehner involutions
Class	620c	Isogeny class
Conductor	620	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-39680 = -1 · 28 · 5 · 31	Discriminant
Eigenvalues	2- -3 5- -2  2  2 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,8,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	221184/155	j-invariant
L	1.471896729826	L(r)(E,1)/r!
Ω	2.3002922131673	Real period
R	0.21329126815579	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2480o1 9920d1 5580c1 3100c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 620c1

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
-	-3	-	-2	2	2	-3	-3	-4	-4	+	-7	-3	-5	-6	1	-11	8	4	15	-13	-12	7	-18	10

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Quadratic twists for elliptic curve 620c1

-4	8	-3	5	-7	-11	13	-31
2480o1	9920d1	5580c1	3100c1	30380c1	75020c1	104780j1	19220d1

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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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