Cremona's table of elliptic curves

42 = 2 · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+	Signs for the Atkin-Lehner involutions
Class	42a	Isogeny class
Conductor	42	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-4218578658 = -1 · 2 · 316 · 72	Discriminant
Eigenvalues	2- 3+ -2 7+ -4  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,386,1277]	[a1,a2,a3,a4,a6]
j	6359387729183/4218578658	j-invariant
L	0.8688618643742	L(r)(E,1)/r!
Ω	0.8688618643742	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	336d6 1344g6 126b6 1050h6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 42a6

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	+	-4	6	2	-4	8	-2	0	-10	-6	-4	0	6	4	6	4	8	10	0	-4	-6	-14

---

Quadratic twists for elliptic curve 42a6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
336d6	1344g6	126b6	1050h6	294c6	5082i6	7098b6	12138bb6	15162l6	22218z5	35322p5	40362bc5	57498b5	70602bn5	77658t5	92778m5	117978f5

---

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