Cremona's table of elliptic curves

714 = 2 · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	714a	Isogeny class
Conductor	714	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-626805817344 = -1 · 214 · 38 · 73 · 17	Discriminant
Eigenvalues	2+ 3+  2 7+ -6  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3334,81940]	[a1,a2,a3,a4,a6]
Generators	[13:196:1]	Generators of the group modulo torsion
j	-4100379159705193/626805817344	j-invariant
L	1.5642040390478	L(r)(E,1)/r!
Ω	0.88148938851514	Real period
R	1.7745012695873	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5712w1 22848x1 2142q1 17850cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 714a1

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	+	-6	0	+	-2	0	-4	0	8	2	-4	-8	-14	-6	-10	0	-12	14	4	-6	-14	-6

---

Quadratic twists for elliptic curve 714a1

-4	8	-3	5	-7	-11	13	17
5712w1	22848x1	2142q1	17850cf1	4998w1	86394ci1	120666bp1	12138m1

---

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