Cremona's table of elliptic curves

30576 = 2⁴ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	30576bk	Isogeny class
Conductor	30576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	-678672746938368 = -1 · 228 · 34 · 74 · 13	Discriminant
Eigenvalues	2- 3+ -4 7+  1 13+  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-59600,-5719104]	[a1,a2,a3,a4,a6]
j	-2380771254001/69009408	j-invariant
L	0.61006422059092	L(r)(E,1)/r!
Ω	0.15251605514767	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3822bb1 122304gt1 91728dm1 30576df1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bk1

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
-	+	-4	+	1	+	3	1	-6	-9	8	-8	0	-10	11	1	5	-15	5	15	2	2	8	0	10

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Quadratic twists for elliptic curve 30576bk1

-4	8	-3	-7
3822bb1	122304gt1	91728dm1	30576df1

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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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