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	64	Product of Tamagawa factors cp
Δ	8978700616704 = 210 · 32 · 78 · 132	Discriminant
Eigenvalues	2+ 3+ -2 7-  4 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5504,64464]	[a1,a2,a3,a4,a6]
Generators	[-40:468:1]	Generators of the group modulo torsion
j	153091012/74529	j-invariant
L	4.4535093959354	L(r)(E,1)/r!
Ω	0.65016133758253	Real period
R	1.712463175869	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15288n2 122304hg2 91728bo2 4368f2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576k2

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 30576k2

-4	8	-3	-7
15288n2	122304hg2	91728bo2	4368f2

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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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