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	16	Product of Tamagawa factors cp
Δ	10989225 = 32 · 52 · 132 · 172	Discriminant
Eigenvalues	-1 3+ 5+ -4 -4 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-71,-196]	[a1,a2,a3,a4,a6]
Generators	[-7:7:1] [-6:10:1]	Generators of the group modulo torsion
j	39616946929/10989225	j-invariant
L	2.2772855863689	L(r)(E,1)/r!
Ω	1.678988880507	Real period
R	1.3563434593338	Regulator
r	2	Rank of the group of rational points
S	0.9999999999996	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	53040co2 9945k2 16575h2 43095f2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3315b2

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

---

Quadratic twists for elliptic curve 3315b2

-4	-3	5	13	17
53040co2	9945k2	16575h2	43095f2	56355x2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations