Cremona's table of elliptic curves

30300 = 2² · 3 · 5² · 101

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 101+	Signs for the Atkin-Lehner involutions
Class	30300l	Isogeny class
Conductor	30300	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	9576	Modular degree for the optimal curve
Δ	-121200 = -1 · 24 · 3 · 52 · 101	Discriminant
Eigenvalues	2- 3- 5+ -2  5  6  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-538,-4987]	[a1,a2,a3,a4,a6]
Generators	[203580363:748103687:6128487]	Generators of the group modulo torsion
j	-43133781760/303	j-invariant
L	7.070821619328	L(r)(E,1)/r!
Ω	0.49557176879392	Real period
R	14.268007309086	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	121200by1 90900n1 30300e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 30300l1

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	5	6	0	-7	-4	2	-8	-5	3	-7	10	13	-3	8	-12	4	-16	0	4	-3	-9

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Quadratic twists for elliptic curve 30300l1

-4	-3	5
121200by1	90900n1	30300e1

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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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