Cremona's table of elliptic curves

17760 = 2⁵ · 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	17760a	Isogeny class
Conductor	17760	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	374625000000000 = 29 · 34 · 512 · 37	Discriminant
Eigenvalues	2+ 3+ 5+  0  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37176,2609460]	[a1,a2,a3,a4,a6]
Generators	[-156:2142:1]	Generators of the group modulo torsion
j	11098222096711112/731689453125	j-invariant
L	4.0899565368815	L(r)(E,1)/r!
Ω	0.5261597413546	Real period
R	3.886611056893	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	17760j2 35520cz3 53280br3 88800cd3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760a3

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	0	2	6	4	-4	-6	-8	+	10	4	0	-6	4	-6	4	-16	10	-16	4	-14	-2

---

Quadratic twists for elliptic curve 17760a3

-4	8	-3	5
17760j2	35520cz3	53280br3	88800cd3

---

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