Cremona's table of elliptic curves

504 = 2³ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+	Signs for the Atkin-Lehner involutions
Class	504c	Isogeny class
Conductor	504	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3584673792 = 211 · 36 · 74	Discriminant
Eigenvalues	2+ 3- -2 7+  4  2  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-531,3726]	[a1,a2,a3,a4,a6]
j	11090466/2401	j-invariant
L	1.3257183030913	L(r)(E,1)/r!
Ω	1.3257183030913	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1008h3 4032g4 56a3 12600cc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504c4

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

---

Quadratic twists for elliptic curve 504c4

-4	8	-3	5	-7	-11	13
1008h3	4032g4	56a3	12600cc4	3528k3	60984ch3	85176ce3

---

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