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
deg	32	Modular degree for the optimal curve
Δ	9225 = 32 · 52 · 41	Discriminant
Eigenvalues	-1 3+ 5+  0  2  0  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6,-6]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	24137569/9225	j-invariant
L	1.2171094498295	L(r)(E,1)/r!
Ω	3.1476280914773	Real period
R	0.38667511359584	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	9840w1 39360be1 1845g1 3075i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 615a1

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 615a1

-4	8	-3	5	-7	-11	13	41
9840w1	39360be1	1845g1	3075i1	30135bg1	74415c1	103935e1	25215e1

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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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