Cremona's table of elliptic curves

6370 = 2 · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	6370k	Isogeny class
Conductor	6370	Conductor
∏ cp	432	Product of Tamagawa factors cp
deg	266112	Modular degree for the optimal curve
Δ	-5312198338202828800 = -1 · 224 · 52 · 78 · 133	Discriminant
Eigenvalues	2- -2 5+ 7+  3 13- -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7352941,7674505425]	[a1,a2,a3,a4,a6]
Generators	[14018:1623711:1]	Generators of the group modulo torsion
j	-7626453723007966609/921488588800	j-invariant
L	4.036757369112	L(r)(E,1)/r!
Ω	0.23242854333214	Real period
R	0.3618278144794	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	50960r1 57330cb1 31850c1 6370w1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370k1

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	+	+	3	-	-3	-1	-6	3	-4	2	-6	8	3	3	-9	5	5	-15	-4	8	-12	-12	-4

---

Quadratic twists for elliptic curve 6370k1

-4	-3	5	-7	13
50960r1	57330cb1	31850c1	6370w1	82810y1

---

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