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	12915r	Isogeny class
Conductor	12915	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	256000	Modular degree for the optimal curve
Δ	-3.0798194894345E+19	Discriminant
Eigenvalues	0 3- 5- 7-  3  0 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-3469332,2501526037]	[a1,a2,a3,a4,a6]
Generators	[4357:264757:1]	Generators of the group modulo torsion
j	-6334812566762194468864/42247180925026875	j-invariant
L	4.4227968843685	L(r)(E,1)/r!
Ω	0.20983105620901	Real period
R	0.13173684118412	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	4305a1 64575o1 90405n1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12915r1

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	0	-3	2	-4	7	-9	-3	-	-5	1	-2	0	-7	6	-5	-3	-6	-2	-18	-6

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Quadratic twists for elliptic curve 12915r1

-3	5	-7
4305a1	64575o1	90405n1

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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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