Cremona's table of elliptic curves

5415 = 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	5415c	Isogeny class
Conductor	5415	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1319555807905275 = 310 · 52 · 197	Discriminant
Eigenvalues	1 3+ 5+ -2 -6  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-27443,75438]	[a1,a2,a3,a4,a6]
Generators	[-58:1244:1] [-2:362:1]	Generators of the group modulo torsion
j	48587168449/28048275	j-invariant
L	4.7343683912427	L(r)(E,1)/r!
Ω	0.41017901837717	Real period
R	2.8855500763881	Regulator
r	2	Rank of the group of rational points
S	0.99999999999967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	86640dk2 16245l2 27075r2 285a2	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 5415c2

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	+	+	-2	-6	0	-6	-	-8	-4	0	-4	0	-2	-8	-2	-12	2	8	-16	14	-8	0	0	12

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Quadratic twists for elliptic curve 5415c2

-4	-3	5	-19
86640dk2	16245l2	27075r2	285a2

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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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