Cremona's table of elliptic curves

7072 = 2⁵ · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	7072f	Isogeny class
Conductor	7072	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	183872 = 26 · 132 · 17	Discriminant
Eigenvalues	2- -2 -2 -2  0 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-14,-8]	[a1,a2,a3,a4,a6]
Generators	[-3:4:1] [-2:4:1]	Generators of the group modulo torsion
j	5088448/2873	j-invariant
L	3.6198274405382	L(r)(E,1)/r!
Ω	2.6438150855392	Real period
R	1.369168161698	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7072d1 14144t1 63648g1 91936h1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7072f1

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	-2	0	+	+	-4	-4	0	-2	-2	-8	-8	-12	10	-4	8	4	-10	-4	-16	-4	6	-4

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Quadratic twists for elliptic curve 7072f1

-4	8	-3	13	17
7072d1	14144t1	63648g1	91936h1	120224e1

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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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