Cremona's table of elliptic curves

35 = 5 · 7

Field	Data	Notes
Atkin-Lehner	5+ 7-	Signs for the Atkin-Lehner involutions
Class	35a	Isogeny class
Conductor	35	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-42875 = -1 · 53 · 73	Discriminant
Eigenvalues	0  1 5+ 7- -3  5  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,9,1]	[a1,a2,a3,a4,a6]
j	71991296/42875	j-invariant
L	0.70291123913491	L(r)(E,1)/r!
Ω	2.1087337174047	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	560c2 2240m2 315a2 175b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 35a1

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	1	+	-	-3	5	3	2	-6	3	-4	2	-12	-10	9	12	0	8	-4	0	2	-1	12	-12	-1

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Quadratic twists for elliptic curve 35a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
560c2	2240m2	315a2	175b2	245c2	4235b2	5915f2	10115g2	12635a2	18515i2	29435c2	33635b2	47915c2	58835a2	64715e2	77315f2	98315i2	121835c2

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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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