Cremona's table of elliptic curves

1035 = 3² · 5 · 23

Field	Data	Notes
Atkin-Lehner	3- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	1035b	Isogeny class
Conductor	1035	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-3592245915 = -1 · 310 · 5 · 233	Discriminant
Eigenvalues	-2 3- 5+  3 -2 -2 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,267,2344]	[a1,a2,a3,a4,a6]
Generators	[16:-104:1]	Generators of the group modulo torsion
j	2887553024/4927635	j-invariant
L	1.3553264872317	L(r)(E,1)/r!
Ω	0.96101079847978	Real period
R	0.23505224731011	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	16560bl1 66240dd1 345e1 5175g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1035b1

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	-2	-2	-5	-2	-	5	3	-7	11	-8	-8	-5	1	-8	-9	-1	10	0	-15	0	-10

---

Quadratic twists for elliptic curve 1035b1

-4	8	-3	5	-7	-11	-23
16560bl1	66240dd1	345e1	5175g1	50715bu1	125235ba1	23805x1

---

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