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	30576cz	Isogeny class
Conductor	30576	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-3787889322672 = -1 · 24 · 35 · 78 · 132	Discriminant
Eigenvalues	2- 3-  2 7-  0 13-  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,2483,81458]	[a1,a2,a3,a4,a6]
Generators	[2:294:1]	Generators of the group modulo torsion
j	899022848/2012283	j-invariant
L	7.8856680143341	L(r)(E,1)/r!
Ω	0.546125088266	Real period
R	1.4439307374382	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7644c1 122304fj1 91728fq1 4368s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576cz1

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	-	0	-	4	-8	-6	2	-8	-2	2	4	2	-6	-6	2	4	4	6	0	10	-10	2

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Quadratic twists for elliptic curve 30576cz1

-4	8	-3	-7
7644c1	122304fj1	91728fq1	4368s1

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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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