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	1680n	Isogeny class
Conductor	1680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3982970880 = -1 · 212 · 34 · 5 · 74	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,280,2352]	[a1,a2,a3,a4,a6]
Generators	[2:54:1]	Generators of the group modulo torsion
j	590589719/972405	j-invariant
L	2.5500823063495	L(r)(E,1)/r!
Ω	0.95073484096146	Real period
R	1.3411112102354	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	105a4 6720bx4 5040bd4 8400cg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680n4

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	-6	2	8	-8	-2	-4	-2	-6	-4	-8	10	-4	-2	-4	12	-2	-8	4	-6	-18

---

Quadratic twists for elliptic curve 1680n4

-4	8	-3	5	-7
105a4	6720bx4	5040bd4	8400cg4	11760ce4

---

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