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	2178c	Isogeny class
Conductor	2178	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-227838196155042 = -1 · 2 · 312 · 118	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,4878,713070]	[a1,a2,a3,a4,a6]
Generators	[-41:686:1]	Generators of the group modulo torsion
j	9938375/176418	j-invariant
L	2.2422631081335	L(r)(E,1)/r!
Ω	0.416267437432	Real period
R	1.3466481560306	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17424bm2 69696bn2 726h2 54450fr2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2178c2

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

---

Quadratic twists for elliptic curve 2178c2

-4	8	-3	5	-7	-11
17424bm2	69696bn2	726h2	54450fr2	106722cu2	198b2

---

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