Cremona's table of elliptic curves

12390 = 2 · 3 · 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7- 59+	Signs for the Atkin-Lehner involutions
Class	12390n	Isogeny class
Conductor	12390	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	3673331197200 = 24 · 33 · 52 · 78 · 59	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4031,-36331]	[a1,a2,a3,a4,a6]
Generators	[-59:50:1]	Generators of the group modulo torsion
j	7243839850989169/3673331197200	j-invariant
L	5.4381172732745	L(r)(E,1)/r!
Ω	0.63219011844964	Real period
R	2.1505070684317	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	99120cn1 37170p1 61950t1 86730cv1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12390n1

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
-	+	+	-	-4	2	-6	-4	0	10	4	10	10	-12	-8	10	+	-6	4	4	-6	-16	-12	10	-6

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Quadratic twists for elliptic curve 12390n1

-4	-3	5	-7
99120cn1	37170p1	61950t1	86730cv1

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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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