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	504g	Isogeny class
Conductor	504	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-756142128 = -1 · 24 · 39 · 74	Discriminant
Eigenvalues	2- 3- -2 7-  0  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-66,-1339]	[a1,a2,a3,a4,a6]
j	-2725888/64827	j-invariant
L	1.3835976409306	L(r)(E,1)/r!
Ω	0.69179882046528	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	1008e1 4032o1 168b1 12600m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 504g1

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

---

Quadratic twists for elliptic curve 504g1

-4	8	-3	5	-7	-11	13
1008e1	4032o1	168b1	12600m1	3528y1	60984z1	85176o1

---

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