Cremona's table of elliptic curves

6825 = 3 · 5² · 7 · 13

Class	r	Atkin-Lehner	Eigenvalues
6825a (4 curves)	1	3+ 5+ 7+ 13+	-1 3+ 5+ 7+  0 13+ -2  4
Curve Equation t Generators 6825a1 [1,1,1,162,906] 2 [4:38:1] 6825a2 [1,1,1,-963,7656] 4 [-14:143:1] 6825a3 [1,1,1,-5838,-167844] 2 [-39:68:1] 6825a4 [1,1,1,-14088,637656] 2 [75:62:1]
6825b (4 curves)	0	3+ 5+ 7+ 13-	1 3+ 5+ 7+ -4 13- -2  0
Curve Equation t 6825b1 [1,1,0,-25525,-1565000] 2 6825b2 [1,1,0,-46650,1371375] 4 6825b3 [1,1,0,-604025,180288750] 2 6825b4 [1,1,0,172725,10804500] 2
6825c (4 curves)	0	3+ 5+ 7- 13+	-1 3+ 5+ 7-  4 13+  2  4
Curve Equation t 6825c1 [1,1,1,-3563,-83344] 2 6825c2 [1,1,1,-3688,-77344] 4 6825c3 [1,1,1,-15063,627906] 2 6825c4 [1,1,1,5687,-396094] 2
6825d (4 curves)	1	3+ 5+ 7- 13-	-1 3+ 5+ 7-  4 13- -6  8
Curve Equation t Generators 6825d1 [1,1,1,-713,1406] 4 [-24:85:1] 6825d2 [1,1,1,-6838,-219094] 4 [-49:60:1] 6825d3 [1,1,1,-109213,-13937344] 2 [3470:34511:8] 6825d4 [1,1,1,-2463,-490344] 2 [105:597:1]
6825e (1 curve)	1	3+ 5+ 7- 13-	-2 3+ 5+ 7- -2 13-  0  1
Curve Equation t Generators 6825e1 [0,-1,1,63492,-19806082] 1 [858:-25799:1]
6825f (2 curves)	1	3+ 5- 7- 13+	-1 3+ 5- 7-  0 13+ -6  2
Curve Equation t Generators 6825f1 [1,1,1,-98,-394] 2 [-6:7:1] 6825f2 [1,1,1,77,-1444] 2 [25:117:1]
6825g (2 curves)	1	3+ 5- 7- 13+	-1 3+ 5- 7- -6 13+  0  2
Curve Equation t Generators 6825g1 [1,1,1,-124263,16614156] 2 [60:3032:1] 6825g2 [1,1,1,-18638,44076656] 2 [-114:6745:1]
6825h (6 curves)	0	3- 5+ 7+ 13+	1 3- 5+ 7+  4 13+ -2 -4
Curve Equation t 6825h1 [1,0,1,3749,485273] 2 6825h2 [1,0,1,-74376,7360273] 4 6825h3 [1,0,1,-227501,-32758477] 4 6825h4 [1,0,1,-1171251,487791523] 2 6825h5 [1,0,1,-3416876,-2431168477] 2 6825h6 [1,0,1,511874,-201335977] 2
6825i (1 curve)	0	3- 5+ 7+ 13+	2 3- 5+ 7+ -2 13+  4  3
Curve Equation t 6825i1 [0,1,1,-658,7219] 1
6825j (4 curves)	1	3- 5+ 7- 13+	-1 3- 5+ 7-  0 13+ -2 -4
Curve Equation t Generators 6825j1 [1,0,0,-5838,-144333] 2 [-33:129:1] 6825j2 [1,0,0,-26963,1566792] 4 [-53:1714:1] 6825j3 [1,0,0,-421838,105418917] 2 [157:6484:1] 6825j4 [1,0,0,29912,7311167] 2 [38:2897:1]
6825k (2 curves)	0	3- 5- 7+ 13-	1 3- 5- 7+  0 13-  6  2
Curve Equation t 6825k1 [1,0,1,-2451,-44327] 2 6825k2 [1,0,1,1924,-184327] 2
6825l (2 curves)	0	3- 5- 7+ 13-	1 3- 5- 7+ -6 13-  0  2
Curve Equation t 6825l1 [1,0,1,-4971,132913] 2 6825l2 [1,0,1,-746,352613] 2

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

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