Cremona's table of elliptic curves

30600 = 2³ · 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	30600ca	Isogeny class
Conductor	30600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	331776	Modular degree for the optimal curve
Δ	205817134781250000 = 24 · 318 · 59 · 17	Discriminant
Eigenvalues	2- 3- 5+  0  4 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-214050,-31248875]	[a1,a2,a3,a4,a6]
Generators	[-5910:61075:27]	Generators of the group modulo torsion
j	5951163357184/1129312125	j-invariant
L	5.5411353908585	L(r)(E,1)/r!
Ω	0.224878000174	Real period
R	6.1601572703543	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	61200bd1 10200r1 6120m1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 30600ca1

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	4	-6	+	4	-8	6	4	-2	-6	4	4	10	-12	6	4	0	-14	-4	16	-10	-6

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Quadratic twists for elliptic curve 30600ca1

-4	-3	5
61200bd1	10200r1	6120m1

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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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