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	300d	Isogeny class
Conductor	300	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-2592000 = -1 · 28 · 34 · 53	Discriminant
Eigenvalues	2- 3+ 5- -4 -4  0 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,72]	[a1,a2,a3,a4,a6]
Generators	[2:10:1]	Generators of the group modulo torsion
j	5488/81	j-invariant
L	1.3840260496868	L(r)(E,1)/r!
Ω	1.9034784804244	Real period
R	0.24236786562431	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	1200s2 4800bg2 900h2 300c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 300d2

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 300d2

-4	8	-3	5	-7	-11	13	17	-19
1200s2	4800bg2	900h2	300c2	14700bv2	36300bf2	50700q2	86700cb2	108300ct2

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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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