Cremona's table of elliptic curves

1683 = 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	1683h	Isogeny class
Conductor	1683	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-280416411 = -1 · 36 · 113 · 172	Discriminant
Eigenvalues	0 3- -3  2 11+  2 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,96,-720]	[a1,a2,a3,a4,a6]
Generators	[6:8:1]	Generators of the group modulo torsion
j	134217728/384659	j-invariant
L	2.1941824774334	L(r)(E,1)/r!
Ω	0.89107583020674	Real period
R	1.231198514791	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	26928bz1 107712cp1 187a1 42075t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683h1

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	-	-3	2	+	2	-	2	3	6	-7	-7	-12	-10	0	-6	3	8	-7	9	2	8	-6	-15	11

---

Quadratic twists for elliptic curve 1683h1

-4	8	-3	5	-7	-11	17
26928bz1	107712cp1	187a1	42075t1	82467q1	18513m1	28611r1

---

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