Cremona's table of elliptic curves

5304 = 2³ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	5304k	Isogeny class
Conductor	5304	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	90058355712 = 210 · 34 · 13 · 174	Discriminant
Eigenvalues	2- 3+ -2 -4 -4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1144,4060]	[a1,a2,a3,a4,a6]
Generators	[-18:136:1] [-10:120:1]	Generators of the group modulo torsion
j	161838334948/87947613	j-invariant
L	3.7129282267513	L(r)(E,1)/r!
Ω	0.93560928579419	Real period
R	0.99211505356112	Regulator
r	2	Rank of the group of rational points
S	0.99999999999984	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10608l4 42432t3 15912h4 68952h3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 5304k3

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	-4	-	-	-4	-8	-2	-4	-6	-6	-4	-4	14	0	-10	-12	-8	-10	8	-8	6	-10

---

Quadratic twists for elliptic curve 5304k3

-4	8	-3	13	17
10608l4	42432t3	15912h4	68952h3	90168be3

---

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