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	504f	Isogeny class
Conductor	504	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	244944 = 24 · 37 · 7	Discriminant
Eigenvalues	2- 3- -2 7+  0 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-66,205]	[a1,a2,a3,a4,a6]
Generators	[-7:18:1]	Generators of the group modulo torsion
j	2725888/21	j-invariant
L	1.8042640646924	L(r)(E,1)/r!
Ω	3.1386213067464	Real period
R	1.1497175914878	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	1008g1 4032f1 168a1 12600q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504f1

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	+	0	-2	-6	-4	4	-6	-8	-10	10	12	8	-6	-4	-10	12	-4	2	8	-4	-6	10

---

Quadratic twists for elliptic curve 504f1

-4	8	-3	5	-7	-11	13
1008g1	4032f1	168a1	12600q1	3528x1	60984bh1	85176bc1

---

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