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	620b	Isogeny class
Conductor	620	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	48050000 = 24 · 55 · 312	Discriminant
Eigenvalues	2-  0 5- -2 -4 -4  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1052,13129]	[a1,a2,a3,a4,a6]
Generators	[-12:155:1]	Generators of the group modulo torsion
j	8047314026496/3003125	j-invariant
L	2.051852494783	L(r)(E,1)/r!
Ω	1.974759104463	Real period
R	0.13853858529855	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2480n1 9920a1 5580d1 3100a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 620b1

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
-	0	-	-2	-4	-4	0	0	-4	2	+	8	6	-8	-6	-8	4	2	-2	0	-4	0	-8	6	-2

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Quadratic twists for elliptic curve 620b1

-4	8	-3	5	-7	-11	13	-31
2480n1	9920a1	5580d1	3100a1	30380b1	75020b1	104780h1	19220c1

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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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