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	30576k	Isogeny class
Conductor	30576	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-609170303379456 = -1 · 211 · 34 · 710 · 13	Discriminant
Eigenvalues	2+ 3+ -2 7-  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19976,472144]	[a1,a2,a3,a4,a6]
Generators	[58:1350:1]	Generators of the group modulo torsion
j	3658553134/2528253	j-invariant
L	4.4535093959354	L(r)(E,1)/r!
Ω	0.32508066879126	Real period
R	3.4249263517381	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15288n4 122304hg3 91728bo3 4368f4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576k3

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	-	-2	4	4	10	8	2	-10	-4	-8	-6	-8	-2	8	-8	-6	-8	8	-2	-14

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Quadratic twists for elliptic curve 30576k3

-4	8	-3	-7
15288n4	122304hg3	91728bo3	4368f4

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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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