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	700c	Isogeny class
Conductor	700	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	-2800 = -1 · 24 · 52 · 7	Discriminant
Eigenvalues	2-  0 5+ 7- -5 -6  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5,5]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-34560/7	j-invariant
L	2.1348487950155	L(r)(E,1)/r!
Ω	4.3423658688886	Real period
R	0.16387754659358	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	2800p1 11200q1 6300r1 700f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 700c1

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 700c1

-4	8	-3	5	-7	-11	13
2800p1	11200q1	6300r1	700f1	4900d1	84700g1	118300e1

---

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