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	510d	Isogeny class
Conductor	510	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	936360000 = 26 · 34 · 54 · 172	Discriminant
Eigenvalues	2- 3+ 5+ -4 -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-421,-3157]	[a1,a2,a3,a4,a6]
Generators	[-13:24:1]	Generators of the group modulo torsion
j	8253429989329/936360000	j-invariant
L	2.1812264076948	L(r)(E,1)/r!
Ω	1.0617409547254	Real period
R	0.68479553887008	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4080bb2 16320bn2 1530f2 2550k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 510d2

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
-	+	+	-4	-4	-2	-	-4	-4	2	4	-6	2	-12	8	-2	12	2	4	-4	-14	-12	-4	10	18

---

Quadratic twists for elliptic curve 510d2

-4	8	-3	5	-7	-11	13	17
4080bb2	16320bn2	1530f2	2550k2	24990cd2	61710c2	86190r2	8670bb2

---

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