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	30576q	Isogeny class
Conductor	30576	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	184320	Modular degree for the optimal curve
Δ	244202905516752 = 24 · 310 · 76 · 133	Discriminant
Eigenvalues	2+ 3+ -4 7-  2 13- -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31915,2072386]	[a1,a2,a3,a4,a6]
Generators	[278:3822:1]	Generators of the group modulo torsion
j	1909913257984/129730653	j-invariant
L	3.2854480532783	L(r)(E,1)/r!
Ω	0.54489431205051	Real period
R	2.0098381041483	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15288bg1 122304ht1 91728cb1 624e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576q1

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
+	+	-4	-	2	-	-2	8	-4	-6	-4	6	12	-4	-6	-2	-14	-10	4	-2	2	8	14	0	10

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Quadratic twists for elliptic curve 30576q1

-4	8	-3	-7
15288bg1	122304ht1	91728cb1	624e1

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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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