Cremona's table of elliptic curves

7854 = 2 · 3 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11- 17+	Signs for the Atkin-Lehner involutions
Class	7854m	Isogeny class
Conductor	7854	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	9984	Modular degree for the optimal curve
Δ	-122435503344 = -1 · 24 · 312 · 7 · 112 · 17	Discriminant
Eigenvalues	2- 3+  2 7- 11-  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-672,17841]	[a1,a2,a3,a4,a6]
j	-33563861678593/122435503344	j-invariant
L	3.6602523835476	L(r)(E,1)/r!
Ω	0.91506309588689	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	62832bk1 23562n1 54978cd1 86394d1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854m1

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	+	-4	4	-10	0	10	6	4	8	6	0	2	4	4	14	-8	0	-18	-10

---

Quadratic twists for elliptic curve 7854m1

-4	-3	-7	-11
62832bk1	23562n1	54978cd1	86394d1

---

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