Cremona's table of elliptic curves

29680 = 2⁴ · 5 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 5- 7- 53+	Signs for the Atkin-Lehner involutions
Class	29680f	Isogeny class
Conductor	29680	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	12672	Modular degree for the optimal curve
Δ	-629216000 = -1 · 28 · 53 · 7 · 532	Discriminant
Eigenvalues	2+  1 5- 7-  5 -1 -7 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,175,875]	[a1,a2,a3,a4,a6]
Generators	[10:265:8]	Generators of the group modulo torsion
j	2302045184/2457875	j-invariant
L	7.4110515816686	L(r)(E,1)/r!
Ω	1.075444462947	Real period
R	1.1485253829163	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14840c1 118720t1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 29680f1

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	-	-	5	-1	-7	-2	8	-5	2	-12	0	8	-1	+	-14	0	-2	16	-14	13	-4	14	-7

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Quadratic twists for elliptic curve 29680f1

-4	8
14840c1	118720t1

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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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