Cremona's table of elliptic curves

3515 = 5 · 19 · 37

Field	Data	Notes
Atkin-Lehner	5+ 19- 37-	Signs for the Atkin-Lehner involutions
Class	3515a	Isogeny class
Conductor	3515	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	896	Modular degree for the optimal curve
Δ	120546925 = 52 · 194 · 37	Discriminant
Eigenvalues	0 -1 5+  1 -5  0  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-151,-434]	[a1,a2,a3,a4,a6]
Generators	[-4:9:1]	Generators of the group modulo torsion
j	383290015744/120546925	j-invariant
L	2.0970100476322	L(r)(E,1)/r!
Ω	1.3948326489918	Real period
R	0.18792667073251	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	56240j1 31635i1 17575a1 66785b1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3515a1

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	-1	+	1	-5	0	4	-	8	4	-6	-	-9	10	-3	11	-12	-2	-4	9	13	14	-9	-10	-18

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Quadratic twists for elliptic curve 3515a1

-4	-3	5	-19
56240j1	31635i1	17575a1	66785b1

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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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