Cremona's table of elliptic curves

5082 = 2 · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	5082d	Isogeny class
Conductor	5082	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-103306896 = -1 · 24 · 32 · 72 · 114	Discriminant
Eigenvalues	2+ 3+ -3 7+ 11- -5 -1 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-849,9189]	[a1,a2,a3,a4,a6]
Generators	[-27:129:1] [-18:147:1]	Generators of the group modulo torsion
j	-4631003113/7056	j-invariant
L	2.8226458477125	L(r)(E,1)/r!
Ω	1.8851533393635	Real period
R	0.062387627148937	Regulator
r	2	Rank of the group of rational points
S	0.99999999999917	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656dn1 15246bl1 127050ig1 35574bl1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5082d1

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
+	+	-3	+	-	-5	-1	-6	-4	-1	-6	-3	-9	10	-10	3	-2	-6	8	-6	-6	-6	-16	-17	13

---

Quadratic twists for elliptic curve 5082d1

-4	-3	5	-7	-11
40656dn1	15246bl1	127050ig1	35574bl1	5082x1

---

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