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	1785o	Isogeny class
Conductor	1785	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	91556816413125 = 3 · 54 · 7 · 178	Discriminant
Eigenvalues	-1 3- 5- 7- -4 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-71740,-7387525]	[a1,a2,a3,a4,a6]
Generators	[490:8425:1]	Generators of the group modulo torsion
j	40832710302042509761/91556816413125	j-invariant
L	2.3616383858566	L(r)(E,1)/r!
Ω	0.29175458563484	Real period
R	1.0118257356255	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	28560cv6 114240bh6 5355f5 8925b5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1785o5

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
-1	-	-	-	-4	-2	-	-4	-8	6	0	-10	-6	-4	0	6	-4	6	4	8	2	-16	-12	-6	10

---

Quadratic twists for elliptic curve 1785o5

-4	8	-3	5	-7	17
28560cv6	114240bh6	5355f5	8925b5	12495b5	30345c6

---

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