Cremona's table of elliptic curves

2838 = 2 · 3 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 43-	Signs for the Atkin-Lehner involutions
Class	2838f	Isogeny class
Conductor	2838	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	589220020224 = 222 · 33 · 112 · 43	Discriminant
Eigenvalues	2- 3- -2 -2 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2244,17424]	[a1,a2,a3,a4,a6]
Generators	[0:132:1]	Generators of the group modulo torsion
j	1249695959916097/589220020224	j-invariant
L	4.8305275903402	L(r)(E,1)/r!
Ω	0.81928516340848	Real period
R	0.17866749025543	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22704t1 90816e1 8514b1 70950f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2838f1

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	-2	-	-2	-2	-4	2	-6	4	-4	-2	-	-6	-12	-12	8	-4	12	2	-12	16	-2	-18

---

Quadratic twists for elliptic curve 2838f1

-4	8	-3	5	-11	-43
22704t1	90816e1	8514b1	70950f1	31218g1	122034c1

---

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