Cremona's table of elliptic curves

3174 = 2 · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	3174g	Isogeny class
Conductor	3174	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	-490294864368 = -1 · 24 · 32 · 237	Discriminant
Eigenvalues	2- 3+ -2  0  0 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1576,-22903]	[a1,a2,a3,a4,a6]
Generators	[111:1183:1]	Generators of the group modulo torsion
j	2924207/3312	j-invariant
L	3.8470357162768	L(r)(E,1)/r!
Ω	0.50221184895923	Real period
R	3.830092543863	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	25392be1 101568x1 9522e1 79350y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3174g1

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	0	0	-2	-2	8	-	-2	-8	-2	10	-8	8	-2	-4	-2	-8	0	-6	-8	16	-18	-10

---

Quadratic twists for elliptic curve 3174g1

-4	8	-3	5	-23
25392be1	101568x1	9522e1	79350y1	138c1

---

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