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	7072b	Isogeny class
Conductor	7072	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-1285277274112 = -1 · 212 · 13 · 176	Discriminant
Eigenvalues	2+ -2  4  0 -4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6481,-210273]	[a1,a2,a3,a4,a6]
Generators	[1594:20315:8]	Generators of the group modulo torsion
j	-7351176280384/313788397	j-invariant
L	3.608298490949	L(r)(E,1)/r!
Ω	0.26538115187374	Real period
R	4.5322215053987	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7072h2 14144c1 63648w2 91936r2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7072b2

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	4	0	-4	-	-	-4	-2	-10	4	8	0	4	0	10	-12	2	-4	0	-8	10	-4	-10	4

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Quadratic twists for elliptic curve 7072b2

-4	8	-3	13	17
7072h2	14144c1	63648w2	91936r2	120224c2

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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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