Cremona's table of elliptic curves

12360 = 2³ · 3 · 5 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 103-	Signs for the Atkin-Lehner involutions
Class	12360b	Isogeny class
Conductor	12360	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-14238720 = -1 · 210 · 33 · 5 · 103	Discriminant
Eigenvalues	2+ 3+ 5-  3  0 -4 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-40,220]	[a1,a2,a3,a4,a6]
Generators	[2:12:1]	Generators of the group modulo torsion
j	-7086244/13905	j-invariant
L	4.4396956828964	L(r)(E,1)/r!
Ω	1.9829747342357	Real period
R	1.119453416689	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24720d1 98880v1 37080q1 61800m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12360b1

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
+	+	-	3	0	-4	-5	-2	-6	6	1	-3	8	6	3	12	0	-13	12	-12	9	-10	-2	1	10

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Quadratic twists for elliptic curve 12360b1

-4	8	-3	5
24720d1	98880v1	37080q1	61800m1

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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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