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	30576bf	Isogeny class
Conductor	30576	Conductor
∏ cp	264	Product of Tamagawa factors cp
deg	152064	Modular degree for the optimal curve
Δ	-273393340286976 = -1 · 211 · 311 · 73 · 133	Discriminant
Eigenvalues	2+ 3- -3 7- -3 13- -7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-31712,2304084]	[a1,a2,a3,a4,a6]
Generators	[100:-378:1] [-194:1092:1]	Generators of the group modulo torsion
j	-5020930768142/389191959	j-invariant
L	8.3708021487029	L(r)(E,1)/r!
Ω	0.53966640330452	Real period
R	0.058754044540199	Regulator
r	2	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15288z1 122304fp1 91728bu1 30576g1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bf1

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
+	-	-3	-	-3	-	-7	-1	-7	-7	-10	3	0	-7	4	-6	-6	-7	-8	-6	1	4	-10	-16	2

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Quadratic twists for elliptic curve 30576bf1

-4	8	-3	-7
15288z1	122304fp1	91728bu1	30576g1

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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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