Cremona's table of elliptic curves

35175 = 3 · 5² · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 67+	Signs for the Atkin-Lehner involutions
Class	35175z	Isogeny class
Conductor	35175	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	-49721513856328125 = -1 · 310 · 57 · 74 · 672	Discriminant
Eigenvalues	-1 3- 5+ 7-  4 -4 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-414838,103364417]	[a1,a2,a3,a4,a6]
Generators	[437:-2581:1]	Generators of the group modulo torsion
j	-505288421809878169/3182176886805	j-invariant
L	4.5860120354751	L(r)(E,1)/r!
Ω	0.35854436756485	Real period
R	0.31976600738582	Regulator
r	1	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	105525w2 7035a2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 35175z2

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

---

Quadratic twists for elliptic curve 35175z2

-3	5
105525w2	7035a2

---

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