Cremona's table of elliptic curves

1170 = 2 · 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	1170i	Isogeny class
Conductor	1170	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-15992437500 = -1 · 22 · 39 · 56 · 13	Discriminant
Eigenvalues	2- 3+ 5+ -4  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2243,-40769]	[a1,a2,a3,a4,a6]
Generators	[926:8443:8]	Generators of the group modulo torsion
j	-63378025803/812500	j-invariant
L	3.2585381990432	L(r)(E,1)/r!
Ω	0.34661391199482	Real period
R	4.7005300224243	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	9360bb3 37440s3 1170b1 5850b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1170i3

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
-	+	+	-4	0	-	-6	-4	6	-6	-10	-10	-6	-4	12	12	-12	-10	14	0	-16	8	12	6	8

---

Quadratic twists for elliptic curve 1170i3

-4	8	-3	5	-7	13
9360bb3	37440s3	1170b1	5850b3	57330dh3	15210e3

---

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