Cremona's table of elliptic curves

5175 = 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	5175i	Isogeny class
Conductor	5175	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-7368310546875 = -1 · 38 · 511 · 23	Discriminant
Eigenvalues	0 3- 5+ -1 -4  0  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-164550,25692156]	[a1,a2,a3,a4,a6]
Generators	[230:112:1]	Generators of the group modulo torsion
j	-43258336804864/646875	j-invariant
L	2.9256288309886	L(r)(E,1)/r!
Ω	0.67976527060402	Real period
R	1.0759702494028	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	82800db1 1725m1 1035c1 119025q1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5175i1

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
0	-	+	-1	-4	0	5	0	-	-5	3	5	-3	4	6	-3	-9	10	7	-7	12	8	-1	-16	6

---

Quadratic twists for elliptic curve 5175i1

-4	-3	5	-23
82800db1	1725m1	1035c1	119025q1

---

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