Cremona's table of elliptic curves

12915 = 3² · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 41+	Signs for the Atkin-Lehner involutions
Class	12915f	Isogeny class
Conductor	12915	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	28245105 = 39 · 5 · 7 · 41	Discriminant
Eigenvalues	-1 3- 5+ 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7268,-236658]	[a1,a2,a3,a4,a6]
j	58235112505081/38745	j-invariant
L	1.034142785262	L(r)(E,1)/r!
Ω	0.51707139263101	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4305d1 64575z1 90405bv1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12915f1

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	-	+	+	4	6	-2	-4	-8	6	-8	6	+	8	0	10	4	-2	-4	16	-2	-4	0	6	10

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Quadratic twists for elliptic curve 12915f1

-3	5	-7
4305d1	64575z1	90405bv1

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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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