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	3315a	Isogeny class
Conductor	3315	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1800	Modular degree for the optimal curve
Δ	-28361896875 = -1 · 35 · 55 · 133 · 17	Discriminant
Eigenvalues	0 3+ 5+  2  2 13+ 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-651,10541]	[a1,a2,a3,a4,a6]
j	-30558612127744/28361896875	j-invariant
L	1.0787671222626	L(r)(E,1)/r!
Ω	1.0787671222626	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53040ck1 9945g1 16575i1 43095g1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3315a1

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	2	+	-	2	2	-1	-5	0	-10	-6	8	-5	3	14	-5	2	-2	12	14	13	6

---

Quadratic twists for elliptic curve 3315a1

-4	-3	5	13	17
53040ck1	9945g1	16575i1	43095g1	56355u1

---

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