Cremona's table of elliptic curves

40800 = 2⁵ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	40800x	Isogeny class
Conductor	40800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-37454400000000 = -1 · 212 · 34 · 58 · 172	Discriminant
Eigenvalues	2+ 3- 5+ -4 -2 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7967,-105937]	[a1,a2,a3,a4,a6]
Generators	[23:300:1] [47:612:1]	Generators of the group modulo torsion
j	873722816/585225	j-invariant
L	9.6179954286924	L(r)(E,1)/r!
Ω	0.36903194305954	Real period
R	0.81446162804975	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	40800bk2 81600q1 122400dv2 8160h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 40800x2

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	-2	-2	+	-4	-8	-6	-10	10	2	-2	-6	-2	-12	-6	-2	-10	10	-10	-18	-2	-2

---

Quadratic twists for elliptic curve 40800x2

-4	8	-3	5
40800bk2	81600q1	122400dv2	8160h2

---

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