Cremona's table of elliptic curves

78897 = 3 · 7 · 13 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 7- 13- 17+	Signs for the Atkin-Lehner involutions
Class	78897g	Isogeny class
Conductor	78897	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	17139436032537 = 33 · 7 · 13 · 178	Discriminant
Eigenvalues	1 3+  0 7- -4 13- 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13155,540072]	[a1,a2,a3,a4,a6]
Generators	[2856:14456:27]	Generators of the group modulo torsion
j	10431681625/710073	j-invariant
L	4.6733996425435	L(r)(E,1)/r!
Ω	0.67988819587584	Real period
R	6.8737766992216	Regulator
r	1	Rank of the group of rational points
S	1.0000000007824	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4641d1	Quadratic twists by: 17

Hecke Eigenvalues for elliptic curve 78897g1

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

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Quadratic twists for elliptic curve 78897g1

17
4641d1

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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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