Cremona's table of elliptic curves

4182 = 2 · 3 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	4182b	Isogeny class
Conductor	4182	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	-19270656 = -1 · 210 · 33 · 17 · 41	Discriminant
Eigenvalues	2+ 3+  1 -3  2  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-427,-3587]	[a1,a2,a3,a4,a6]
Generators	[38:173:1]	Generators of the group modulo torsion
j	-8641627880761/19270656	j-invariant
L	2.2951651888831	L(r)(E,1)/r!
Ω	0.52489472953177	Real period
R	2.1863099967973	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	33456q1 12546o1 104550cf1 71094l1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4182b1

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	2	2	+	0	0	-6	6	-4	+	7	-3	9	-6	-6	-10	8	0	11	6	5	-1

---

Quadratic twists for elliptic curve 4182b1

-4	-3	5	17
33456q1	12546o1	104550cf1	71094l1

---

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