Cremona's table of elliptic curves

3315 = 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	3315b	Isogeny class
Conductor	3315	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-910381875 = -1 · 3 · 54 · 134 · 17	Discriminant
Eigenvalues	-1 3+ 5+ -4 -4 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,184,-1012]	[a1,a2,a3,a4,a6]
Generators	[8:28:1] [11:44:1]	Generators of the group modulo torsion
j	688699320191/910381875	j-invariant
L	2.2772855863689	L(r)(E,1)/r!
Ω	0.8394944402535	Real period
R	1.3563434593338	Regulator
r	2	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53040co3 9945k4 16575h4 43095f3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3315b4

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
-1	+	+	-4	-4	-	+	-4	0	-6	0	-10	-10	-12	-8	2	0	-2	4	-8	2	-4	12	-10	-14

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Quadratic twists for elliptic curve 3315b4

-4	-3	5	13	17
53040co3	9945k4	16575h4	43095f3	56355x3

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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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