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	615b	Isogeny class
Conductor	615	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-56041875 = -1 · 37 · 54 · 41	Discriminant
Eigenvalues	0 3- 5+  0 -1 -4 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,79,-214]	[a1,a2,a3,a4,a6]
Generators	[22:112:1]	Generators of the group modulo torsion
j	53838872576/56041875	j-invariant
L	2.0130725659384	L(r)(E,1)/r!
Ω	1.0766896496168	Real period
R	0.13354906645402	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9840m1 39360q1 1845e1 3075c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 615b1

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
0	-	+	0	-1	-4	-3	-6	0	-5	-5	-3	-	-5	1	6	0	13	2	7	-7	-6	14	6	-6

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Quadratic twists for elliptic curve 615b1

-4	8	-3	5	-7	-11	13	41
9840m1	39360q1	1845e1	3075c1	30135k1	74415h1	103935j1	25215a1

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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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