Cremona's table of elliptic curves

1245 = 3 · 5 · 83

Field	Data	Notes
Atkin-Lehner	3+ 5- 83+	Signs for the Atkin-Lehner involutions
Class	1245b	Isogeny class
Conductor	1245	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	-9195198001003125 = -1 · 32 · 55 · 836	Discriminant
Eigenvalues	-1 3+ 5-  0  2  4 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-19070,-4731568]	[a1,a2,a3,a4,a6]
j	-766967947453190881/9195198001003125	j-invariant
L	0.87471686564835	L(r)(E,1)/r!
Ω	0.17494337312967	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	19920s2 79680t2 3735c2 6225g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1245b2

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	2	4	-4	-2	0	-2	0	2	-2	4	8	14	14	-14	0	16	-8	6	+	6	8

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Quadratic twists for elliptic curve 1245b2

-4	8	-3	5	-7	-83
19920s2	79680t2	3735c2	6225g2	61005s2	103335c2

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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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