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	1680c	Isogeny class
Conductor	1680	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	1890000 = 24 · 33 · 54 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  4 -6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-71,246]	[a1,a2,a3,a4,a6]
j	2508888064/118125	j-invariant
L	1.3015793020499	L(r)(E,1)/r!
Ω	2.6031586040998	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	840h1 6720cn1 5040s1 8400v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1680c1

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	-6	-2	8	-4	6	-4	-2	-2	12	0	2	4	6	4	-8	6	16	4	-18	6

---

Quadratic twists for elliptic curve 1680c1

-4	8	-3	5	-7
840h1	6720cn1	5040s1	8400v1	11760bh1

---

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