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	12180b	Isogeny class
Conductor	12180	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1621862697772800 = 28 · 316 · 52 · 7 · 292	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -2 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-64356,5999256]	[a1,a2,a3,a4,a6]
Generators	[173:116:1]	Generators of the group modulo torsion
j	115148324799160144/6335401163175	j-invariant
L	3.1549878470418	L(r)(E,1)/r!
Ω	0.46746292486853	Real period
R	3.3745861748599	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	48720cj2 36540j2 60900x2 85260z2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12180b2

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

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Quadratic twists for elliptic curve 12180b2

-4	-3	5	-7
48720cj2	36540j2	60900x2	85260z2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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