Cremona's table of elliptic curves

735 = 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	735d	Isogeny class
Conductor	735	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-270225046875 = -1 · 3 · 56 · 78	Discriminant
Eigenvalues	0 3- 5+ 7+  0 -1  6  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-10061,-392605]	[a1,a2,a3,a4,a6]
j	-19539165184/46875	j-invariant
L	1.429863258238	L(r)(E,1)/r!
Ω	0.23831054303967	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11760bk2 47040x2 2205i2 3675a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 735d2

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	-1	6	5	6	-6	5	-7	12	-1	6	0	-6	2	-7	12	11	-13	-12	6	-10

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Quadratic twists for elliptic curve 735d2

-4	8	-3	5	-7	-11	13
11760bk2	47040x2	2205i2	3675a2	735c2	88935bm2	124215ck2

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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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