Cremona's table of elliptic curves

97110 = 2 · 3² · 5 · 13 · 83

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 13- 83+	Signs for the Atkin-Lehner involutions
Class	97110be	Isogeny class
Conductor	97110	Conductor
∏ cp	384	Product of Tamagawa factors cp
deg	2064384	Modular degree for the optimal curve
Δ	-827513396775000000 = -1 · 26 · 37 · 58 · 133 · 832	Discriminant
Eigenvalues	2+ 3- 5- -2 -4 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1243764,535996048]	[a1,a2,a3,a4,a6]
Generators	[-43:-24256:1] [-873:31354:1]	Generators of the group modulo torsion
j	-291884025403196036929/1135134975000000	j-invariant
L	8.4098029479768	L(r)(E,1)/r!
Ω	0.28343972645341	Real period
R	0.30906787535408	Regulator
r	2	Rank of the group of rational points
S	0.99999999994898	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32370v1	Quadratic twists by: -3

Hecke Eigenvalues for elliptic curve 97110be1

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

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Quadratic twists for elliptic curve 97110be1

-3
32370v1

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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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