Cremona's table of elliptic curves

975 = 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	975i	Isogeny class
Conductor	975	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-375378046875 = -1 · 37 · 57 · 133	Discriminant
Eigenvalues	-2 3- 5+ -3 -1 13-  1 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-4758,128144]	[a1,a2,a3,a4,a6]
Generators	[273:-4388:1]	Generators of the group modulo torsion
j	-762549907456/24024195	j-invariant
L	1.4720753966666	L(r)(E,1)/r!
Ω	0.9486309445294	Real period
R	0.018473682736406	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	15600bk1 62400p1 2925n1 195d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 975i1

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	-	+	-3	-1	-	1	-2	3	-2	-6	-11	-5	-4	10	-11	8	13	-12	-5	-10	-3	12	-15	-17

---

Quadratic twists for elliptic curve 975i1

-4	8	-3	5	-7	-11	13
15600bk1	62400p1	2925n1	195d1	47775l1	117975bn1	12675ba1

---

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