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	30576cr	Isogeny class
Conductor	30576	Conductor
∏ cp	144	Product of Tamagawa factors cp
deg	248832	Modular degree for the optimal curve
Δ	-6905114109444096 = -1 · 215 · 39 · 77 · 13	Discriminant
Eigenvalues	2- 3- -3 7- -3 13+  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10568,3979604]	[a1,a2,a3,a4,a6]
Generators	[86:-2352:1] [-106:1296:1]	Generators of the group modulo torsion
j	270840023/14329224	j-invariant
L	8.3792477277208	L(r)(E,1)/r!
Ω	0.3195607693969	Real period
R	0.1820912511921	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3822f1 122304gj1 91728en1 4368p1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576cr1

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	+	3	-7	-9	-9	-4	-7	-12	1	0	-6	12	1	-14	-12	7	10	-6	6	10

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Quadratic twists for elliptic curve 30576cr1

-4	8	-3	-7
3822f1	122304gj1	91728en1	4368p1

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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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