Cremona's table of elliptic curves

27900 = 2² · 3² · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 31+	Signs for the Atkin-Lehner involutions
Class	27900g	Isogeny class
Conductor	27900	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	35145964800 = 28 · 311 · 52 · 31	Discriminant
Eigenvalues	2- 3- 5+ -4 -3  2 -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-840,-2540]	[a1,a2,a3,a4,a6]
Generators	[-19:81:1]	Generators of the group modulo torsion
j	14049280/7533	j-invariant
L	4.0340690068962	L(r)(E,1)/r!
Ω	0.94347974993182	Real period
R	1.0689336488641	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	111600fl1 9300k1 27900q1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 27900g1

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	-3	2	-3	-3	3	7	+	-10	2	10	-10	1	10	6	-5	6	14	-16	-9	17	13

---

Quadratic twists for elliptic curve 27900g1

-4	-3	5
111600fl1	9300k1	27900q1

---

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