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	3315f	Isogeny class
Conductor	3315	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-10989225 = -1 · 32 · 52 · 132 · 172	Discriminant
Eigenvalues	-1 3- 5- -2  0 13+ 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,25,-150]	[a1,a2,a3,a4,a6]
Generators	[7:16:1]	Generators of the group modulo torsion
j	1723683599/10989225	j-invariant
L	2.646082587776	L(r)(E,1)/r!
Ω	1.1358288692798	Real period
R	0.58241224962301	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	53040br2 9945e2 16575c2 43095k2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3315f2

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	-	-	-2	0	+	+	2	0	-10	-4	2	6	6	-8	-2	10	10	-8	-12	-6	-14	16	-10	2

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Quadratic twists for elliptic curve 3315f2

-4	-3	5	13	17
53040br2	9945e2	16575c2	43095k2	56355a2

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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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