Cremona's table of elliptic curves

707 = 7 · 101

Field	Data	Notes
Atkin-Lehner	7+ 101-	Signs for the Atkin-Lehner involutions
Class	707a	Isogeny class
Conductor	707	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	104	Modular degree for the optimal curve
Δ	4949 = 72 · 101	Discriminant
Eigenvalues	-2 -2 -3 7+ -4 -1 -7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-12,12]	[a1,a2,a3,a4,a6]
Generators	[-4:3:1] [0:3:1]	Generators of the group modulo torsion
j	207474688/4949	j-invariant
L	0.97385134602465	L(r)(E,1)/r!
Ω	4.3145192961889	Real period
R	0.11285745632049	Regulator
r	2	Rank of the group of rational points
S	0.99999999999749	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11312l1 45248d1 6363a1 17675h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 707a1

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

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Quadratic twists for elliptic curve 707a1

-4	8	-3	5	-7	-11	13	101
11312l1	45248d1	6363a1	17675h1	4949c1	85547g1	119483b1	71407e1

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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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