Cremona's table of elliptic curves

1653 = 3 · 19 · 29

Field	Data	Notes
Atkin-Lehner	3+ 19+ 29-	Signs for the Atkin-Lehner involutions
Class	1653a	Isogeny class
Conductor	1653	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-11648691 = -1 · 36 · 19 · 292	Discriminant
Eigenvalues	0 3+ -3 -1 -5 -4 -7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-27,182]	[a1,a2,a3,a4,a6]
Generators	[-4:14:1] [0:13:1]	Generators of the group modulo torsion
j	-2258403328/11648691	j-invariant
L	2.2488411552331	L(r)(E,1)/r!
Ω	1.9611889766098	Real period
R	0.28666808528563	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26448u1 105792w1 4959c1 41325j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1653a1

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
0	+	-3	-1	-5	-4	-7	+	-8	-	-4	-2	0	5	1	-2	0	-3	10	-6	3	-12	12	-10	14

---

Quadratic twists for elliptic curve 1653a1

-4	8	-3	5	-7	-19	29
26448u1	105792w1	4959c1	41325j1	80997t1	31407e1	47937e1

---

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