Cremona's table of elliptic curves

1680 = 2⁴ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	1680m	Isogeny class
Conductor	1680	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	36578304000000 = 216 · 36 · 56 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9240,-176400]	[a1,a2,a3,a4,a6]
Generators	[-70:350:1]	Generators of the group modulo torsion
j	21302308926361/8930250000	j-invariant
L	2.5723360911699	L(r)(E,1)/r!
Ω	0.50545013393832	Real period
R	0.8481997591358	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	210b2 6720bw2 5040bc2 8400cf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680m2

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

---

Quadratic twists for elliptic curve 1680m2

-4	8	-3	5	-7
210b2	6720bw2	5040bc2	8400cf2	11760cd2

---

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