Cremona's table of elliptic curves

1947 = 3 · 11 · 59

Field	Data	Notes
Atkin-Lehner	3+ 11- 59+	Signs for the Atkin-Lehner involutions
Class	1947d	Isogeny class
Conductor	1947	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-1419363 = -1 · 37 · 11 · 59	Discriminant
Eigenvalues	2 3+ -2  0 11- -1  7  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-434,3629]	[a1,a2,a3,a4,a6]
j	-9061356040192/1419363	j-invariant
L	2.6080338660926	L(r)(E,1)/r!
Ω	2.6080338660926	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	31152y1 124608bf1 5841h1 48675r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1947d1

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
2	+	-2	0	-	-1	7	2	3	2	10	12	3	4	-3	2	+	-2	2	-2	-3	4	6	13	-2

---

Quadratic twists for elliptic curve 1947d1

-4	8	-3	5	-7	-11	-59
31152y1	124608bf1	5841h1	48675r1	95403m1	21417b1	114873d1

---

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