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	30576u	Isogeny class
Conductor	30576	Conductor
∏ cp	216	Product of Tamagawa factors cp
deg	120960	Modular degree for the optimal curve
Δ	-16356866512896 = -1 · 211 · 39 · 74 · 132	Discriminant
Eigenvalues	2+ 3- -3 7+ -5 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40392,3117204]	[a1,a2,a3,a4,a6]
Generators	[324:4914:1] [114:-84:1]	Generators of the group modulo torsion
j	-1482171386066/3326427	j-invariant
L	8.2672903709473	L(r)(E,1)/r!
Ω	0.69714540141496	Real period
R	0.054901735535231	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15288c1 122304et1 91728q1 30576o1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576u1

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	+	-5	+	-2	0	-6	-3	-1	-8	-12	0	-8	-3	-9	4	-12	10	-10	-15	11	-16	-7

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Quadratic twists for elliptic curve 30576u1

-4	8	-3	-7
15288c1	122304et1	91728q1	30576o1

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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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