Cremona's table of elliptic curves

713 = 23 · 31

Field	Data	Notes
Atkin-Lehner	23- 31-	Signs for the Atkin-Lehner involutions
Class	713a	Isogeny class
Conductor	713	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	-713 = -1 · 23 · 31	Discriminant
Eigenvalues	1  1  0 -3 -4  2  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1,1]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	-15625/713	j-invariant
L	2.7924101607346	L(r)(E,1)/r!
Ω	4.2159507276509	Real period
R	0.66234411669477	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	11408d1 45632k1 6417g1 17825a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 713a1

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	1	0	-3	-4	2	3	-4	-	-6	-	6	-1	4	6	13	-14	5	-13	-14	0	-8	4	-2	-6

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Quadratic twists for elliptic curve 713a1

-4	8	-3	5	-7	-11	13	-23	-31
11408d1	45632k1	6417g1	17825a1	34937a1	86273c1	120497d1	16399c1	22103b1

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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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