Cremona's table of elliptic curves

6630 = 2 · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13- 17+	Signs for the Atkin-Lehner involutions
Class	6630s	Isogeny class
Conductor	6630	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-259683840000 = -1 · 212 · 33 · 54 · 13 · 172	Discriminant
Eigenvalues	2- 3+ 5-  4 -4 13- 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1580,4757]	[a1,a2,a3,a4,a6]
j	436192097814719/259683840000	j-invariant
L	3.6001440622176	L(r)(E,1)/r!
Ω	0.60002401036959	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	53040cz1 19890l1 33150q1 86190c1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630s1

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
-	+	-	4	-4	-	+	8	-4	2	0	6	-6	4	0	-2	-4	6	12	0	6	0	12	10	-18

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Quadratic twists for elliptic curve 6630s1

-4	-3	5	13	17
53040cz1	19890l1	33150q1	86190c1	112710cv1

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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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