Cremona's table of elliptic curves

7828 = 2² · 19 · 103

Field	Data	Notes
Atkin-Lehner	2- 19+ 103+	Signs for the Atkin-Lehner involutions
Class	7828a	Isogeny class
Conductor	7828	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	31312 = 24 · 19 · 103	Discriminant
Eigenvalues	2- -1 -2 -1  0 -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9,10]	[a1,a2,a3,a4,a6]
Generators	[-2:4:1] [1:1:1]	Generators of the group modulo torsion
j	5619712/1957	j-invariant
L	4.2788996379126	L(r)(E,1)/r!
Ω	3.4040612705604	Real period
R	0.41899947325844	Regulator
r	2	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31312s1 125248o1 70452g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7828a1

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	-2	-1	0	-6	-2	+	3	-10	3	-9	-6	0	4	-13	-10	-7	-7	9	4	2	-15	-5	0

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Quadratic twists for elliptic curve 7828a1

-4	8	-3
31312s1	125248o1	70452g1

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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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