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	735b	Isogeny class
Conductor	735	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4704	Modular degree for the optimal curve
Δ	-386108355976875 = -1 · 37 · 54 · 710	Discriminant
Eigenvalues	-2 3+ 5+ 7- -6  3  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-15206,-1184338]	[a1,a2,a3,a4,a6]
j	-1376628736/1366875	j-invariant
L	0.4133357624511	L(r)(E,1)/r!
Ω	0.20666788122555	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	11760cj1 47040dr1 2205m1 3675m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 735b1

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	+	+	-	-6	3	4	-1	-4	-8	-1	7	6	1	-2	4	8	14	7	6	-1	-1	-2	12	6

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Quadratic twists for elliptic curve 735b1

-4	8	-3	5	-7	-11	13
11760cj1	47040dr1	2205m1	3675m1	735f1	88935r1	124215bh1

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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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