Cremona's table of elliptic curves

97216 = 2⁶ · 7² · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	97216o	Isogeny class
Conductor	97216	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	428319522684928 = 224 · 77 · 31	Discriminant
Eigenvalues	2+  0  0 7-  2 -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-22540,839664]	[a1,a2,a3,a4,a6]
Generators	[133:441:1]	Generators of the group modulo torsion
j	41063625/13888	j-invariant
L	5.2287806063917	L(r)(E,1)/r!
Ω	0.4877996220645	Real period
R	2.679778928128	Regulator
r	1	Rank of the group of rational points
S	1.0000000024791	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97216bj1 3038d1 13888a1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 97216o1

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	0	-	2	-2	-2	-6	0	-8	-	8	10	6	4	-4	6	6	4	-8	-14	-16	8	6	-14

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Quadratic twists for elliptic curve 97216o1

-4	8	-7
97216bj1	3038d1	13888a1

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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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