Cremona's table of elliptic curves

315 = 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	315b	Isogeny class
Conductor	315	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-708883245 = -1 · 310 · 5 · 74	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 -6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,157,992]	[a1,a2,a3,a4,a6]
Generators	[0:31:1]	Generators of the group modulo torsion
j	590589719/972405	j-invariant
L	1.1391577592797	L(r)(E,1)/r!
Ω	1.0978140327141	Real period
R	0.25941501140757	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	5040bd4 20160ch4 105a4 1575f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 315b4

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	-6	-2	-8	-8	2	4	-2	6	4	-8	-10	-4	-2	4	12	-2	8	4	6	-18

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Quadratic twists for elliptic curve 315b4

-4	8	-3	5	-7	-11	13	17	-19
5040bd4	20160ch4	105a4	1575f4	2205k4	38115k3	53235bc3	91035bi3	113715t3

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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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