Cremona's table of elliptic curves

49 = 7²

Field	Data	Notes
Atkin-Lehner	7-	Signs for the Atkin-Lehner involutions
Class	49a	Isogeny class
Conductor	49	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	-343 = -1 · 73	Discriminant
Eigenvalues	1  0  0 7-  4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2,-1]	[a1,a2,a3,a4,a6]
j	-3375	j-invariant
L	0.96665585280841	L(r)(E,1)/r!
Ω	1.9333117056168	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	784h1 3136d1 441d1 1225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 49a1

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	0	-	4	0	0	0	8	2	0	-6	0	-12	0	-10	0	0	4	16	0	8	0	0	0

---

Quadratic twists for elliptic curve 49a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
784h1	3136d1	441d1	1225b1	49a3	5929e1	8281g1	14161a1	17689h1	25921a1	41209e1	47089a1	67081c1	82369a1	90601c1	108241a1

---

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