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	64	Product of Tamagawa factors cp
Δ	143659209867264 = 214 · 32 · 78 · 132	Discriminant
Eigenvalues	2- 3- -2 7-  4 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21184,1030196]	[a1,a2,a3,a4,a6]
Generators	[-68:1470:1]	Generators of the group modulo torsion
j	2181825073/298116	j-invariant
L	5.8404935226502	L(r)(E,1)/r!
Ω	0.55839172185869	Real period
R	2.6148728992656	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	3822x2 122304fi2 91728fo2 4368o2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576dc2

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 30576dc2

-4	8	-3	-7
3822x2	122304fi2	91728fo2	4368o2

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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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