Cremona's table of elliptic curves

3030 = 2 · 3 · 5 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 101+	Signs for the Atkin-Lehner involutions
Class	3030b	Isogeny class
Conductor	3030	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-757500000 = -1 · 25 · 3 · 57 · 101	Discriminant
Eigenvalues	2+ 3+ 5+  1 -2 -1  1 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-253,-2147]	[a1,a2,a3,a4,a6]
Generators	[21:38:1]	Generators of the group modulo torsion
j	-1802041022809/757500000	j-invariant
L	2.0167820424546	L(r)(E,1)/r!
Ω	0.58617573019895	Real period
R	3.4405758180573	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24240bg1 96960bo1 9090bc1 15150bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3030b1

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	-2	-1	1	-6	8	8	3	-6	-2	-13	7	1	-4	-13	10	12	-3	1	3	-5	12

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Quadratic twists for elliptic curve 3030b1

-4	8	-3	5
24240bg1	96960bo1	9090bc1	15150bk1

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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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