Cremona's table of elliptic curves

12615 = 3 · 5 · 29²

Field	Data	Notes
Atkin-Lehner	3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	12615f	Isogeny class
Conductor	12615	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	97565895227025 = 38 · 52 · 296	Discriminant
Eigenvalues	1 3- 5-  0  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-113553,-14729777]	[a1,a2,a3,a4,a6]
Generators	[-42726:30355:216]	Generators of the group modulo torsion
j	272223782641/164025	j-invariant
L	7.237290736105	L(r)(E,1)/r!
Ω	0.26008545559776	Real period
R	6.9566469215583	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	37845d6 63075c6 15a2	Quadratic twists by: -3 5 29

Hecke Eigenvalues for elliptic curve 12615f5

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

---

Quadratic twists for elliptic curve 12615f5

-3	5	29
37845d6	63075c6	15a2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations