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	12180f	Isogeny class
Conductor	12180	Conductor
∏ cp	240	Product of Tamagawa factors cp
Δ	1.2956365440637E+20	Discriminant
Eigenvalues	2- 3+ 5- 7- -2 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-56096500,161733315352]	[a1,a2,a3,a4,a6]
Generators	[4449:14210:1]	Generators of the group modulo torsion
j	76258990297490164969896016/506108025024879375	j-invariant
L	4.0787881662435	L(r)(E,1)/r!
Ω	0.16532979915611	Real period
R	0.41117695126779	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	48720cs2 36540h2 60900s2 85260t2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12180f2

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	-4	-4	4	-	4	-2	8	6	-8	-6	4	4	0	-4	16	6	12	-4	-8

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Quadratic twists for elliptic curve 12180f2

-4	-3	5	-7
48720cs2	36540h2	60900s2	85260t2

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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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