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	30576dc	Isogeny class
Conductor	30576	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	-15607547014864896 = -1 · 213 · 34 · 77 · 134	Discriminant
Eigenvalues	2- 3- -2 7-  4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,33696,5530356]	[a1,a2,a3,a4,a6]
Generators	[-78:1560:1]	Generators of the group modulo torsion
j	8780064047/32388174	j-invariant
L	5.8404935226502	L(r)(E,1)/r!
Ω	0.27919586092935	Real period
R	1.3074364496328	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3822x4 122304fi3 91728fo3 4368o4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576dc3

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

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Quadratic twists for elliptic curve 30576dc3

-4	8	-3	-7
3822x4	122304fi3	91728fo3	4368o4

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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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