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	3634a	Isogeny class
Conductor	3634	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	71592	Modular degree for the optimal curve
Δ	264210720009224192 = 238 · 233 · 79	Discriminant
Eigenvalues	2+  2 -4  0 -2  2  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-194787,21903245]	[a1,a2,a3,a4,a6]
Generators	[-67172941077:5320727156720:876467493]	Generators of the group modulo torsion
j	817348184878300169401/264210720009224192	j-invariant
L	2.8588818023563	L(r)(E,1)/r!
Ω	0.28647217662407	Real period
R	19.959228404285	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	29072o1 116288g1 32706g1 90850n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3634a1

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	-4	0	-2	2	2	6	+	-8	8	-2	-2	4	0	2	-14	6	-10	-8	-6	+	-6	18	-2

---

Quadratic twists for elliptic curve 3634a1

-4	8	-3	5	-23
29072o1	116288g1	32706g1	90850n1	83582j1

---

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