Cremona's table of elliptic curves

13300 = 2² · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	13300f	Isogeny class
Conductor	13300	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	-66500000000 = -1 · 28 · 59 · 7 · 19	Discriminant
Eigenvalues	2- -1 5+ 7+ -6  4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,492,11512]	[a1,a2,a3,a4,a6]
Generators	[-3:100:1]	Generators of the group modulo torsion
j	3286064/16625	j-invariant
L	3.1205335912107	L(r)(E,1)/r!
Ω	0.79185772534448	Real period
R	1.9703877927396	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53200cg1 119700w1 2660g1 93100j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 13300f1

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
-	-1	+	+	-6	4	-3	-	-3	0	2	7	-3	1	12	3	0	-10	16	3	7	8	6	-6	-8

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Quadratic twists for elliptic curve 13300f1

-4	-3	5	-7
53200cg1	119700w1	2660g1	93100j1

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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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