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	30576i	Isogeny class
Conductor	30576	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-329967247663872 = -1 · 28 · 33 · 710 · 132	Discriminant
Eigenvalues	2+ 3+  0 7- -2 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3348,878256]	[a1,a2,a3,a4,a6]
Generators	[68:980:1]	Generators of the group modulo torsion
j	-137842000/10955763	j-invariant
L	4.3646198491877	L(r)(E,1)/r!
Ω	0.44631126716799	Real period
R	2.4448295227245	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	15288k2 122304gv2 91728be2 4368l2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576i2

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
+	+	0	-	-2	-	2	0	0	-6	4	-2	0	-12	2	6	-6	14	12	10	10	0	-2	4	10

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Quadratic twists for elliptic curve 30576i2

-4	8	-3	-7
15288k2	122304gv2	91728be2	4368l2

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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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