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	2574a	Isogeny class
Conductor	2574	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-126817726464 = -1 · 212 · 39 · 112 · 13	Discriminant
Eigenvalues	2+ 3+  2 -2 11+ 13+ -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,309,-17083]	[a1,a2,a3,a4,a6]
Generators	[49:313:1]	Generators of the group modulo torsion
j	165469149/6443008	j-invariant
L	2.5590703843704	L(r)(E,1)/r!
Ω	0.50122645154515	Real period
R	2.5528085922854	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20592u1 82368m1 2574s1 64350cu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2574a1

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	+	+	-4	2	4	4	-6	-2	-2	-4	8	-4	-4	-14	2	0	-10	-16	12	-10	14

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Quadratic twists for elliptic curve 2574a1

-4	8	-3	5	-7	-11	13
20592u1	82368m1	2574s1	64350cu1	126126n1	28314bh1	33462cb1

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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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