Cremona's table of elliptic curves

3634 = 2 · 23 · 79

Field	Data	Notes
Atkin-Lehner	2+ 23+ 79-	Signs for the Atkin-Lehner involutions
Class	3634b	Isogeny class
Conductor	3634	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	668656 = 24 · 232 · 79	Discriminant
Eigenvalues	2+ -3 -1 -1 -4 -5  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-220,1312]	[a1,a2,a3,a4,a6]
Generators	[-12:52:1] [4:20:1]	Generators of the group modulo torsion
j	1180597050009/668656	j-invariant
L	2.1026402206706	L(r)(E,1)/r!
Ω	2.8372899956949	Real period
R	0.18526835676496	Regulator
r	2	Rank of the group of rational points
S	0.99999999999928	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29072k1 116288k1 32706h1 90850o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3634b1

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	-1	-1	-4	-5	0	0	+	-4	2	-6	-8	-4	1	-2	11	-10	-8	1	6	-	-12	-9	-13

---

Quadratic twists for elliptic curve 3634b1

-4	8	-3	5	-23
29072k1	116288k1	32706h1	90850o1	83582e1

---

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