Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 13-	Signs for the Atkin-Lehner involutions
Class	2730x	Isogeny class
Conductor	2730	Conductor
∏ cp	768	Product of Tamagawa factors cp
Δ	2833965225000000 = 26 · 34 · 58 · 72 · 134	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-36530,-828673]	[a1,a2,a3,a4,a6]
Generators	[-163:991:1]	Generators of the group modulo torsion
j	5391051390768345121/2833965225000000	j-invariant
L	4.2863873932156	L(r)(E,1)/r!
Ω	0.36618768628013	Real period
R	0.24386329935284	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840cg3 87360ck3 8190n4 13650z3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730x3

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	-	-6	-4	-8	-10	0	-2	-6	12	8	-2	4	-2	-4	8	-14	16	-4	-6	-6

---

Quadratic twists for elliptic curve 2730x3

-4	8	-3	5	-7	13
21840cg3	87360ck3	8190n4	13650z3	19110cp4	35490a3

---

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