Cremona's table of elliptic curves

7735 = 5 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	5- 7+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	7735d	Isogeny class
Conductor	7735	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	7296	Modular degree for the optimal curve
Δ	1127569625 = 53 · 74 · 13 · 172	Discriminant
Eigenvalues	1 -2 5- 7+ -2 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9768,-372367]	[a1,a2,a3,a4,a6]
Generators	[139:910:1]	Generators of the group modulo torsion
j	103056823169347321/1127569625	j-invariant
L	3.2559585768035	L(r)(E,1)/r!
Ω	0.48023493867993	Real period
R	2.2599761870398	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123760bt1 69615k1 38675m1 54145k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7735d1

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

---

Quadratic twists for elliptic curve 7735d1

-4	-3	5	-7	13
123760bt1	69615k1	38675m1	54145k1	100555i1

---

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