Cremona's table of elliptic curves

1830 = 2 · 3 · 5 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 61+	Signs for the Atkin-Lehner involutions
Class	1830f	Isogeny class
Conductor	1830	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-558150000 = -1 · 24 · 3 · 55 · 612	Discriminant
Eigenvalues	2- 3+ 5+  2  2 -6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,114,1083]	[a1,a2,a3,a4,a6]
j	163757102111/558150000	j-invariant
L	2.3231309497664	L(r)(E,1)/r!
Ω	1.1615654748832	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14640bc1 58560bs1 5490j1 9150i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1830f1

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	-6	6	4	-8	8	4	4	6	2	0	-6	-6	+	14	10	6	0	12	12	-6

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Quadratic twists for elliptic curve 1830f1

-4	8	-3	5	-7	61
14640bc1	58560bs1	5490j1	9150i1	89670cm1	111630a1

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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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