Cremona's table of elliptic curves

45472 = 2⁵ · 7² · 29

Field	Data	Notes
Atkin-Lehner	2+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	45472r	Isogeny class
Conductor	45472	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	-484322067522965504 = -1 · 212 · 78 · 295	Discriminant
Eigenvalues	2+  1 -1 7-  3 -3  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,181039,-15498337]	[a1,a2,a3,a4,a6]
Generators	[6123:164836:27]	Generators of the group modulo torsion
j	1361725440704/1005046301	j-invariant
L	6.0331444602181	L(r)(E,1)/r!
Ω	0.16534775957714	Real period
R	1.8243804680659	Regulator
r	1	Rank of the group of rational points
S	0.9999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	45472bh1 90944u1 6496g1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 45472r1

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
+	1	-1	-	3	-3	0	4	-6	-	-7	-10	4	7	9	-5	12	6	14	4	4	-1	12	6	-8

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Quadratic twists for elliptic curve 45472r1

-4	8	-7
45472bh1	90944u1	6496g1

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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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