Cremona's table of elliptic curves

615 = 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	3+ 5+ 41+	Signs for the Atkin-Lehner involutions
Class	615a	Isogeny class
Conductor	615	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-680805 = -1 · 34 · 5 · 412	Discriminant
Eigenvalues	-1 3+ 5+  0  2  0  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,19,-16]	[a1,a2,a3,a4,a6]
Generators	[3:7:1]	Generators of the group modulo torsion
j	756058031/680805	j-invariant
L	1.2171094498295	L(r)(E,1)/r!
Ω	1.5738140457387	Real period
R	0.77335022719168	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9840w2 39360be2 1845g2 3075i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 615a2

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	+	+	0	2	0	0	2	-8	-10	4	2	+	-4	-12	0	0	2	-8	14	-6	10	-12	-18	-16

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Quadratic twists for elliptic curve 615a2

-4	8	-3	5	-7	-11	13	41
9840w2	39360be2	1845g2	3075i2	30135bg2	74415c2	103935e2	25215e2

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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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