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	12075t	Isogeny class
Conductor	12075	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	52992	Modular degree for the optimal curve
Δ	236723626463625 = 33 · 53 · 78 · 233	Discriminant
Eigenvalues	-1 3- 5- 7+  0  4 -8  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-30218,-1883973]	[a1,a2,a3,a4,a6]
Generators	[-83:274:1]	Generators of the group modulo torsion
j	24412471425434357/1893789011709	j-invariant
L	3.4585754837926	L(r)(E,1)/r!
Ω	0.36388299755384	Real period
R	3.1682120416384	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	36225cc1 12075p1 84525ba1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12075t1

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

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Quadratic twists for elliptic curve 12075t1

-3	5	-7
36225cc1	12075p1	84525ba1

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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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