Cremona's table of elliptic curves

2574 = 2 · 3² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	2574b	Isogeny class
Conductor	2574	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	4275640512 = 26 · 33 · 114 · 132	Discriminant
Eigenvalues	2+ 3+ -2 -2 11- 13+ -8  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-14992383,-22339902131]	[a1,a2,a3,a4,a6]
j	13802951728468271053322091/158357056	j-invariant
L	0.61379291805879	L(r)(E,1)/r!
Ω	0.076724114757349	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	20592r2 82368f2 2574q2 64350dc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574b2

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

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Quadratic twists for elliptic curve 2574b2

-4	8	-3	5	-7	-11	13
20592r2	82368f2	2574q2	64350dc2	126126bb2	28314bj2	33462bs2

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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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