Cremona's table of elliptic curves

2698 = 2 · 19 · 71

Field	Data	Notes
Atkin-Lehner	2+ 19- 71+	Signs for the Atkin-Lehner involutions
Class	2698b	Isogeny class
Conductor	2698	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1176	Modular degree for the optimal curve
Δ	-62334592 = -1 · 27 · 193 · 71	Discriminant
Eigenvalues	2+  2  4 -1  4  0  0 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,37,-355]	[a1,a2,a3,a4,a6]
j	5368567751/62334592	j-invariant
L	2.903102682236	L(r)(E,1)/r!
Ω	0.96770089407867	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21584b1 86336b1 24282l1 67450p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2698b1

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	-1	4	0	0	-	5	-3	-2	-3	6	11	-12	-6	-1	6	4	+	13	1	1	-12	15

---

Quadratic twists for elliptic curve 2698b1

-4	8	-3	5	-19
21584b1	86336b1	24282l1	67450p1	51262j1

---

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