Cremona's table of elliptic curves

420 = 2² · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	420d	Isogeny class
Conductor	420	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	8400 = 24 · 3 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5- 7+  2  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5,0]	[a1,a2,a3,a4,a6]
j	1048576/525	j-invariant
L	1.8307443333216	L(r)(E,1)/r!
Ω	3.6614886666431	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	1680o1 6720b1 1260e1 2100e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 420d1

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

---

Quadratic twists for elliptic curve 420d1

-4	8	-3	5	-7	-11	13	17
1680o1	6720b1	1260e1	2100e1	2940b1	50820w1	70980r1	121380i1

---

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