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	24	Product of Tamagawa factors cp
Δ	72900 = 22 · 36 · 52	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-19,26]	[a1,a2,a3,a4,a6]
j	702595369/72900	j-invariant
L	0.55865804320692	L(r)(E,1)/r!
Ω	3.3519482592415	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	12	Number of elements in the torsion subgroup
Twists	240b2 960e2 90c2 150c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 30a2

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 30a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
240b2	960e2	90c2	150c2	1470d2	3630w2	5070v2	8670e2	10830v2	15870u2	25230p2	28830h2	41070bl2	50430f2	55470bc2	66270m2	84270bg2	104430bb2	111630x2

---

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