Cremona's table of elliptic curves

2178 = 2 · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11-	Signs for the Atkin-Lehner involutions
Class	2178a	Isogeny class
Conductor	2178	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	742583750431248 = 24 · 39 · 119	Discriminant
Eigenvalues	2+ 3+  0 -2 11- -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-94947,11208005]	[a1,a2,a3,a4,a6]
j	2714704875/21296	j-invariant
L	1.0176897247645	L(r)(E,1)/r!
Ω	0.50884486238225	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bc3 69696k3 2178g1 54450ed3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178a3

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

---

Quadratic twists for elliptic curve 2178a3

-4	8	-3	5	-7	-11
17424bc3	69696k3	2178g1	54450ed3	106722p3	198c3

---

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