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	12915b	Isogeny class
Conductor	12915	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	-271215 = -1 · 33 · 5 · 72 · 41	Discriminant
Eigenvalues	1 3+ 5- 7-  4 -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,6,23]	[a1,a2,a3,a4,a6]
Generators	[14:45:1]	Generators of the group modulo torsion
j	804357/10045	j-invariant
L	6.3247597682294	L(r)(E,1)/r!
Ω	2.2881307288723	Real period
R	2.7641601454068	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	12915a1 64575b1 90405d1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 12915b1

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	-2	2	-2	0	-10	-4	2	+	-4	8	-12	-12	6	12	12	-8	-12	-12	6	2

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Quadratic twists for elliptic curve 12915b1

-3	5	-7
12915a1	64575b1	90405d1

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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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