Cremona's table of elliptic curves

700 = 2² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	700f	Isogeny class
Conductor	700	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-43750000 = -1 · 24 · 58 · 7	Discriminant
Eigenvalues	2-  0 5- 7+ -5  6 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-125,625]	[a1,a2,a3,a4,a6]
Generators	[0:25:1]	Generators of the group modulo torsion
j	-34560/7	j-invariant
L	2.1076136835671	L(r)(E,1)/r!
Ω	1.941965053202	Real period
R	0.36176649696348	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2800bd1 11200bc1 6300y1 700c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 700f1

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
-	0	-	+	-5	6	-4	-6	-3	-3	2	-7	-4	7	2	10	-14	4	-3	-13	-16	1	-10	10	2

---

Quadratic twists for elliptic curve 700f1

-4	8	-3	5	-7	-11	13
2800bd1	11200bc1	6300y1	700c1	4900r1	84700bj1	118300bm1

---

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