Cremona's table of elliptic curves

1950 = 2 · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	1950z	Isogeny class
Conductor	1950	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-1950 = -1 · 2 · 3 · 52 · 13	Discriminant
Eigenvalues	2- 3- 5+ -4  4 13- -4  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2,2]	[a1,a2,a3,a4,a6]
j	34295/78	j-invariant
L	3.2484492001633	L(r)(E,1)/r!
Ω	3.2484492001633	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15600bn1 62400t1 5850s1 1950c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1950z1

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
-	-	+	-4	4	-	-4	7	4	5	4	9	-5	-10	3	9	-6	4	-7	-15	12	7	6	14	-16

---

Quadratic twists for elliptic curve 1950z1

-4	8	-3	5	-7	13
15600bn1	62400t1	5850s1	1950c1	95550gu1	25350bh1

---

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