Cremona's table of elliptic curves

830 = 2 · 5 · 83

Field	Data	Notes
Atkin-Lehner	2- 5- 83+	Signs for the Atkin-Lehner involutions
Class	830b	Isogeny class
Conductor	830	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-2124800000000 = -1 · 216 · 58 · 83	Discriminant
Eigenvalues	2- -1 5- -3 -5  2 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-11185,456015]	[a1,a2,a3,a4,a6]
Generators	[63:-112:1]	Generators of the group modulo torsion
j	-154751228078685841/2124800000000	j-invariant
L	2.7304793866599	L(r)(E,1)/r!
Ω	0.82728911822914	Real period
R	0.025785266285072	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6640e1 26560a1 7470i1 4150b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 830b1

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
-	-1	-	-3	-5	2	-3	-6	-4	9	-3	-3	-2	0	0	-10	13	5	-10	-6	-16	14	+	8	-8

---

Quadratic twists for elliptic curve 830b1

-4	8	-3	5	-7	-11	-83
6640e1	26560a1	7470i1	4150b1	40670q1	100430r1	68890b1

---

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