Cremona's table of elliptic curves

4515 = 3 · 5 · 7 · 43

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 43-	Signs for the Atkin-Lehner involutions
Class	4515a	Isogeny class
Conductor	4515	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-134615289375 = -1 · 32 · 54 · 7 · 434	Discriminant
Eigenvalues	-1 3+ 5+ 7+ -4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,204,-17532]	[a1,a2,a3,a4,a6]
j	938601300671/134615289375	j-invariant
L	0.49065944924828	L(r)(E,1)/r!
Ω	0.49065944924828	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	72240cr1 13545k1 22575n1 31605bb1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4515a1

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	+	+	+	-4	6	-6	4	0	-2	4	-2	2	-	-4	6	-8	-6	-4	8	-2	-8	-8	-18	2

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Quadratic twists for elliptic curve 4515a1

-4	-3	5	-7
72240cr1	13545k1	22575n1	31605bb1

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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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