Cremona's table of elliptic curves

30324 = 2² · 3 · 7 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 19-	Signs for the Atkin-Lehner involutions
Class	30324d	Isogeny class
Conductor	30324	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	21600	Modular degree for the optimal curve
Δ	-4659707136 = -1 · 28 · 3 · 75 · 192	Discriminant
Eigenvalues	2- 3+  1 7- -1 -4  7 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1260,-17112]	[a1,a2,a3,a4,a6]
j	-2395702096/50421	j-invariant
L	2.0006768636933	L(r)(E,1)/r!
Ω	0.40013537273895	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	121296co1 90972j1 30324j1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 30324d1

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
-	+	1	-	-1	-4	7	-	8	-8	8	-3	-5	8	4	-4	-12	10	-4	4	-14	2	6	-5	8

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Quadratic twists for elliptic curve 30324d1

-4	-3	-19
121296co1	90972j1	30324j1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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