Cremona's table of elliptic curves

300 = 2² · 3 · 5²

Field	Data	Notes
Atkin-Lehner	2- 3- 5-	Signs for the Atkin-Lehner involutions
Class	300c	Isogeny class
Conductor	300	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-40500000000 = -1 · 28 · 34 · 59	Discriminant
Eigenvalues	2- 3- 5-  4 -4  0  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,292,9588]	[a1,a2,a3,a4,a6]
j	5488/81	j-invariant
L	1.7025229103748	L(r)(E,1)/r!
Ω	0.85126145518741	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1200n2 4800o2 900g2 300d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 300c2

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

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Quadratic twists for elliptic curve 300c2

-4	8	-3	5	-7	-11	13	17	-19
1200n2	4800o2	900g2	300d2	14700v2	36300cl2	50700bp2	86700z2	108300bi2

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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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