Cremona's table of elliptic curves

12180 = 2² · 3 · 5 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	12180i	Isogeny class
Conductor	12180	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-9981149472000 = -1 · 28 · 32 · 53 · 72 · 294	Discriminant
Eigenvalues	2- 3- 5- 7+ -6  0 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5220,-211932]	[a1,a2,a3,a4,a6]
Generators	[116:870:1]	Generators of the group modulo torsion
j	-61458003996496/38988865125	j-invariant
L	5.5359285949042	L(r)(E,1)/r!
Ω	0.27300616099088	Real period
R	0.56326858611821	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	48720by2 36540e2 60900d2 85260f2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12180i2

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

---

Quadratic twists for elliptic curve 12180i2

-4	-3	5	-7
48720by2	36540e2	60900d2	85260f2

---

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