Cremona's table of elliptic curves

715 = 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	5- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	715a	Isogeny class
Conductor	715	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-14621035 = -1 · 5 · 113 · 133	Discriminant
Eigenvalues	0 -2 5-  2 11+ 13- -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,45,-129]	[a1,a2,a3,a4,a6]
Generators	[3:6:1]	Generators of the group modulo torsion
j	9855401984/14621035	j-invariant
L	1.5787090658482	L(r)(E,1)/r!
Ω	1.1763200689736	Real period
R	0.4473581376044	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	11440v2 45760h2 6435i2 3575b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 715a2

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
0	-2	-	2	+	-	-3	5	-6	-6	-10	-1	-9	-7	9	-12	0	-4	5	0	2	-10	6	0	17

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Quadratic twists for elliptic curve 715a2

-4	8	-3	5	-7	-11	13
11440v2	45760h2	6435i2	3575b2	35035a2	7865d2	9295b2

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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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