Cremona's table of elliptic curves

3040 = 2⁵ · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	3040d	Isogeny class
Conductor	3040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	2888000 = 26 · 53 · 192	Discriminant
Eigenvalues	2-  0 5+ -2  4 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-173,872]	[a1,a2,a3,a4,a6]
Generators	[-11:38:1]	Generators of the group modulo torsion
j	8947094976/45125	j-invariant
L	2.9961871645744	L(r)(E,1)/r!
Ω	2.5554849161801	Real period
R	1.1724534727652	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	3040c1 6080s2 27360o1 15200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3040d1

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

---

Quadratic twists for elliptic curve 3040d1

-4	8	-3	5	-19
3040c1	6080s2	27360o1	15200e1	57760d1

---

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