Cremona's table of elliptic curves

1230 = 2 · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 41-	Signs for the Atkin-Lehner involutions
Class	1230f	Isogeny class
Conductor	1230	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-900878906250000 = -1 · 24 · 32 · 516 · 41	Discriminant
Eigenvalues	2- 3+ 5-  0  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,23350,456167]	[a1,a2,a3,a4,a6]
j	1407936942337442399/900878906250000	j-invariant
L	2.4823406387639	L(r)(E,1)/r!
Ω	0.31029257984549	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	9840z4 39360bb3 3690d4 6150n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1230f4

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

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Quadratic twists for elliptic curve 1230f4

-4	8	-3	5	-7	41
9840z4	39360bb3	3690d4	6150n4	60270bj3	50430z3

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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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