Cremona's table of elliptic curves

20328 = 2³ · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	20328d	Isogeny class
Conductor	20328	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	126720	Modular degree for the optimal curve
Δ	4573849183352064 = 28 · 35 · 73 · 118	Discriminant
Eigenvalues	2+ 3-  1 7+ 11-  6 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-51465,-3116709]	[a1,a2,a3,a4,a6]
Generators	[-81:726:1]	Generators of the group modulo torsion
j	274717696/83349	j-invariant
L	6.983728709598	L(r)(E,1)/r!
Ω	0.32443619103697	Real period
R	0.35876231354238	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	40656q1 60984bw1 20328ba1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 20328d1

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
+	-	1	+	-	6	-3	4	6	0	-6	-6	-10	-11	-9	-12	7	-2	-9	-2	2	-4	-3	15	-4

---

Quadratic twists for elliptic curve 20328d1

-4	-3	-11
40656q1	60984bw1	20328ba1

---

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