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	48	Product of Tamagawa factors cp
Δ	-5020027429601673216 = -1 · 221 · 33 · 79 · 133	Discriminant
Eigenvalues	2- 3- -3 7- -3 13+  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-95272,-108422476]	[a1,a2,a3,a4,a6]
Generators	[548:2058:1] [2606:131712:1]	Generators of the group modulo torsion
j	-198461344537/10417365504	j-invariant
L	8.3792477277208	L(r)(E,1)/r!
Ω	0.10652025646563	Real period
R	1.6388212607289	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	3822f2 122304gj2 91728en2 4368p2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576cr2

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 30576cr2

-4	8	-3	-7
3822f2	122304gj2	91728en2	4368p2

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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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