Cremona's table of elliptic curves

30 = 2 · 3 · 5

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+	Signs for the Atkin-Lehner involutions
Class	30a	Isogeny class
Conductor	30	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	5314410 = 2 · 312 · 5	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-69,-194]	[a1,a2,a3,a4,a6]
j	35578826569/5314410	j-invariant
L	0.55865804320692	L(r)(E,1)/r!
Ω	1.6759741296207	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	240b5 960e4 90c5 150c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 30a4

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	0	2	6	-4	0	-6	8	2	-6	-4	0	-6	0	-10	-4	0	2	8	12	18	2

---

Quadratic twists for elliptic curve 30a4

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
240b5	960e4	90c5	150c4	1470d5	3630w5	5070v4	8670e4	10830v5	15870u5	25230p4	28830h4	41070bl4	50430f4	55470bc4	66270m4	84270bg4	104430bb4	111630x4

---

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