Cremona's table of elliptic curves

4935 = 3 · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 47+	Signs for the Atkin-Lehner involutions
Class	4935b	Isogeny class
Conductor	4935	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	8736	Modular degree for the optimal curve
Δ	-1619296875 = -1 · 32 · 57 · 72 · 47	Discriminant
Eigenvalues	-2 3+ 5- 7+ -6 -3  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-2000,35156]	[a1,a2,a3,a4,a6]
Generators	[-118000:1066327:4096] [-25:262:1]	Generators of the group modulo torsion
j	-885178441732096/1619296875	j-invariant
L	2.3708586630457	L(r)(E,1)/r!
Ω	1.5010495236725	Real period
R	0.056409547016869	Regulator
r	2	Rank of the group of rational points
S	0.99999999999941	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78960di1 14805f1 24675t1 34545s1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4935b1

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	0	-8	-9	-4	0	-10	-12	-11	+	-6	7	1	4	13	7	-1	6	15	-14

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Quadratic twists for elliptic curve 4935b1

-4	-3	5	-7
78960di1	14805f1	24675t1	34545s1

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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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