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	315a	Isogeny class
Conductor	315	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	-25515 = -1 · 36 · 5 · 7	Discriminant
Eigenvalues	0 3- 5- 7-  3  5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-12,-18]	[a1,a2,a3,a4,a6]
j	-262144/35	j-invariant
L	1.2730829063824	L(r)(E,1)/r!
Ω	1.2730829063824	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5040bk1 20160bq1 35a3 1575e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 315a1

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	-	-	-	3	5	-3	2	6	-3	-4	2	12	-10	-9	-12	0	8	-4	0	2	-1	-12	12	-1

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Quadratic twists for elliptic curve 315a1

-4	8	-3	5	-7	-11	13	17	-19
5040bk1	20160bq1	35a3	1575e1	2205g1	38115y1	53235g1	91035d1	113715bj1

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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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