Cremona's table of elliptic curves

510 = 2 · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	510f	Isogeny class
Conductor	510	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	260100 = 22 · 32 · 52 · 172	Discriminant
Eigenvalues	2- 3- 5+  0  4  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-16,-4]	[a1,a2,a3,a4,a6]
j	454756609/260100	j-invariant
L	2.5858436070631	L(r)(E,1)/r!
Ω	2.5858436070631	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	4080t2 16320r2 1530e2 2550a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510f2

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	4	2	-	-4	4	2	-4	-6	-10	-8	0	6	-8	10	-8	8	-2	4	4	-14	-10

---

Quadratic twists for elliptic curve 510f2

-4	8	-3	5	-7	-11	13	17
4080t2	16320r2	1530e2	2550a2	24990bp2	61710w2	86190bi2	8670r2

---

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