Cremona's table of elliptic curves

9975 = 3 · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	9975o	Isogeny class
Conductor	9975	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	-1066722830415703125 = -1 · 38 · 57 · 78 · 192	Discriminant
Eigenvalues	1 3- 5+ 7-  4  2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,139374,45488773]	[a1,a2,a3,a4,a6]
Generators	[-187:3684:1]	Generators of the group modulo torsion
j	19162556947522799/68270261146605	j-invariant
L	6.7750644074481	L(r)(E,1)/r!
Ω	0.19606484580295	Real period
R	1.0798507089105	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	29925bd5 1995c6 69825p5	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 9975o6

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	2	-2	+	-8	-2	-8	2	-6	-12	0	-6	-4	-2	4	0	-2	0	12	10	-2

---

Quadratic twists for elliptic curve 9975o6

-3	5	-7
29925bd5	1995c6	69825p5

---

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