Cremona's table of elliptic curves

12075 = 3 · 5² · 7 · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 23-	Signs for the Atkin-Lehner involutions
Class	12075i	Isogeny class
Conductor	12075	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	66432687890625 = 38 · 58 · 72 · 232	Discriminant
Eigenvalues	1 3+ 5+ 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-10125,0]	[a1,a2,a3,a4,a6]
Generators	[8100:724950:1]	Generators of the group modulo torsion
j	7347774183121/4251692025	j-invariant
L	4.6006509901413	L(r)(E,1)/r!
Ω	0.52352477045832	Real period
R	4.3939191130476	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	36225bo2 2415h2 84525cj2	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12075i2

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
1	+	+	-	0	-2	6	-4	-	-2	-4	6	2	-4	0	-2	-8	-2	-4	8	2	4	4	-6	14

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Quadratic twists for elliptic curve 12075i2

-3	5	-7
36225bo2	2415h2	84525cj2

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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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