Cremona's table of elliptic curves

7896 = 2³ · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 47+	Signs for the Atkin-Lehner involutions
Class	7896g	Isogeny class
Conductor	7896	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-15472622592 = -1 · 210 · 38 · 72 · 47	Discriminant
Eigenvalues	2- 3+  0 7-  6  4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,552,-3492]	[a1,a2,a3,a4,a6]
Generators	[134:1568:1]	Generators of the group modulo torsion
j	18132345500/15109983	j-invariant
L	4.0802807968311	L(r)(E,1)/r!
Ω	0.68725803585654	Real period
R	2.968521707968	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15792h1 63168bl1 23688j1 55272bm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7896g1

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

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Quadratic twists for elliptic curve 7896g1

-4	8	-3	-7
15792h1	63168bl1	23688j1	55272bm1

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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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