Cremona's table of elliptic curves

4650 = 2 · 3 · 5² · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 31-	Signs for the Atkin-Lehner involutions
Class	4650k	Isogeny class
Conductor	4650	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-858874530000 = -1 · 24 · 3 · 54 · 315	Discriminant
Eigenvalues	2+ 3+ 5-  2  2 -4 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1250,-40700]	[a1,a2,a3,a4,a6]
Generators	[24:50:1]	Generators of the group modulo torsion
j	345168179975/1374199248	j-invariant
L	2.5134886691916	L(r)(E,1)/r!
Ω	0.45087759756517	Real period
R	0.55746585830944	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	37200dq1 13950db1 4650bl2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 4650k1

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	2	-4	-3	0	6	-5	-	-8	12	1	-3	-14	0	-8	2	7	-14	-5	-4	-5	7

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Quadratic twists for elliptic curve 4650k1

-4	-3	5
37200dq1	13950db1	4650bl2

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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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