Cremona's table of elliptic curves

690 = 2 · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 23-	Signs for the Atkin-Lehner involutions
Class	690h	Isogeny class
Conductor	690	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-331200 = -1 · 26 · 32 · 52 · 23	Discriminant
Eigenvalues	2- 3+ 5+ -2 -2 -6 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,4,29]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	6967871/331200	j-invariant
L	2.4704452833257	L(r)(E,1)/r!
Ω	2.3108328098156	Real period
R	0.17817856783293	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	5520y1 22080bp1 2070h1 3450h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690h1

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	-6	-4	0	-	2	0	-8	-6	-4	0	6	0	-8	-4	16	6	14	14	-8	-6

---

Quadratic twists for elliptic curve 690h1

-4	8	-3	5	-7	-11	13	-23
5520y1	22080bp1	2070h1	3450h1	33810dj1	83490g1	116610u1	15870bc1

---

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