Cremona's table of elliptic curves

85 = 5 · 17

Field	Data	Notes
Atkin-Lehner	5+ 17-	Signs for the Atkin-Lehner involutions
Class	85a	Isogeny class
Conductor	85	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	425 = 52 · 17	Discriminant
Eigenvalues	1  2 5+ -2  2  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-8,-13]	[a1,a2,a3,a4,a6]
j	68417929/425	j-invariant
L	1.3976922182719	L(r)(E,1)/r!
Ω	2.7953844365438	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1360g1 5440o1 765c1 425d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 85a1

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	2	+	-2	2	2	-	0	6	-6	-10	2	10	4	12	-10	8	-14	8	-2	-14	-14	4	6	2

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Quadratic twists for elliptic curve 85a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
1360g1	5440o1	765c1	425d1	4165j1	10285e1	14365b1	1445d1	30685a1	44965f1	71485b1	81685b1	116365e1

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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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