Cremona's table of elliptic curves

61504 = 2⁶ · 31²

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	61504h	Isogeny class
Conductor	61504	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	894321072475734016 = 220 · 318	Discriminant
Eigenvalues	2+ -3 -1 -3  3 -5  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4694704108,-123811347857744]	[a1,a2,a3,a4,a6]
Generators	[-539850772784497802:-5062247700736:13646778755273]	Generators of the group modulo torsion
j	51181724570498001/4	j-invariant
L	1.5711301748983	L(r)(E,1)/r!
Ω	0.018238851962572	Real period
R	21.535486144118	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	61504bj2 1922c2 61504bc2	Quadratic twists by: -4 8 -31

Hecke Eigenvalues for elliptic curve 61504h2

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
+	-3	-1	-3	3	-5	3	-7	-4	-2	+	-1	-9	1	-8	3	-3	-6	3	-1	7	1	-5	6	14

---

Quadratic twists for elliptic curve 61504h2

-4	8	-31
61504bj2	1922c2	61504bc2

---

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