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	30576j	Isogeny class
Conductor	30576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-5870592 = -1 · 210 · 32 · 72 · 13	Discriminant
Eigenvalues	2+ 3+  2 7-  3 13-  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72,288]	[a1,a2,a3,a4,a6]
Generators	[6:6:1]	Generators of the group modulo torsion
j	-834148/117	j-invariant
L	6.0364103776546	L(r)(E,1)/r!
Ω	2.3185581132626	Real period
R	0.65087977988618	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15288m1 122304hl1 91728bq1 30576t1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576j1

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	-	3	-	3	7	-8	-1	-4	-2	-2	-2	-7	-3	-3	13	-3	-9	4	2	16	-18	12

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Quadratic twists for elliptic curve 30576j1

-4	8	-3	-7
15288m1	122304hl1	91728bq1	30576t1

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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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