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
deg	24	Modular degree for the optimal curve
Δ	18000 = 24 · 32 · 53	Discriminant
Eigenvalues	2- 3+ 5- -4 -4  0 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13,22]	[a1,a2,a3,a4,a6]
Generators	[7:-15:1]	Generators of the group modulo torsion
j	131072/9	j-invariant
L	1.3840260496868	L(r)(E,1)/r!
Ω	3.8069569608489	Real period
R	0.12118393281215	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	1200s1 4800bg1 900h1 300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 300d1

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 300d1

-4	8	-3	5	-7	-11	13	17	-19
1200s1	4800bg1	900h1	300c1	14700bv1	36300bf1	50700q1	86700cb1	108300ct1

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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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