Cremona's table of elliptic curves

30576 = 2⁴ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	30576bl	Isogeny class
Conductor	30576	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	169344	Modular degree for the optimal curve
Δ	-861955259203584 = -1 · 215 · 33 · 78 · 132	Discriminant
Eigenvalues	2- 3+  3 7+ -3 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17264,-1654848]	[a1,a2,a3,a4,a6]
Generators	[184:1168:1]	Generators of the group modulo torsion
j	-24100657/36504	j-invariant
L	5.8520574965539	L(r)(E,1)/r!
Ω	0.19762656748802	Real period
R	3.7014617840466	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3822bc1 122304go1 91728dr1 30576cs1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bl1

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
-	+	3	+	-3	-	6	4	-6	-9	-5	-4	-12	4	12	-9	9	8	4	-6	14	1	-3	0	5

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Quadratic twists for elliptic curve 30576bl1

-4	8	-3	-7
3822bc1	122304go1	91728dr1	30576cs1

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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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