Cremona's table of elliptic curves

1785 = 3 · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	1785f	Isogeny class
Conductor	1785	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-3346875 = -1 · 32 · 55 · 7 · 17	Discriminant
Eigenvalues	0 3+ 5- 7+ -2  3 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-35,131]	[a1,a2,a3,a4,a6]
Generators	[5:7:1]	Generators of the group modulo torsion
j	-4878401536/3346875	j-invariant
L	2.1951033048894	L(r)(E,1)/r!
Ω	2.3154825153987	Real period
R	0.094801117706192	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	28560ec1 114240da1 5355c1 8925w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785f1

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	3	-	-2	-3	4	-5	-1	11	4	-9	0	-12	-5	-12	-2	-4	-10	-5	-14	-2

---

Quadratic twists for elliptic curve 1785f1

-4	8	-3	5	-7	17
28560ec1	114240da1	5355c1	8925w1	12495i1	30345w1

---

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