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	3515b	Isogeny class
Conductor	3515	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	208703125 = 56 · 192 · 37	Discriminant
Eigenvalues	-2 -3 5- -3 -1 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-307,1950]	[a1,a2,a3,a4,a6]
Generators	[398:-7933:1] [-12:62:1]	Generators of the group modulo torsion
j	3199917920256/208703125	j-invariant
L	1.5915018078999	L(r)(E,1)/r!
Ω	1.7474082407775	Real period
R	0.075898206019417	Regulator
r	2	Rank of the group of rational points
S	0.99999999999821	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56240p1 31635d1 17575c1 66785g1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3515b1

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
-2	-3	-	-3	-1	-4	-6	-	-6	-4	-6	-	9	0	1	1	-6	-10	-12	-13	-11	-14	3	4	16

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Quadratic twists for elliptic curve 3515b1

-4	-3	5	-19
56240p1	31635d1	17575c1	66785g1

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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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