Cremona's table of elliptic curves

12300 = 2² · 3 · 5² · 41

Class	r	Atkin-Lehner	Eigenvalues
12300a (1 curve)	0	2- 3+ 5+ 41+	2- 3+ 5+  4 -5 -4  5 -6
Curve Equation t 12300a1 [0,-1,0,267,86337] 1
12300b (4 curves)	0	2- 3+ 5+ 41+	2- 3+ 5+  4  6 -2  6  2
Curve Equation t 12300b1 [0,-1,0,-36633,-2376738] 2 12300b2 [0,-1,0,54492,-12400488] 2 12300b3 [0,-1,0,-2871633,-1872059238] 2 12300b4 [0,-1,0,-2870508,-1873600488] 2
12300c (1 curve)	0	2- 3+ 5+ 41+	2- 3+ 5+ -4  0 -2 -3  8
Curve Equation t 12300c1 [0,-1,0,1667,4537] 1
12300d (2 curves)	2	2- 3+ 5+ 41+	2- 3+ 5+ -4 -2 -6  2  2
Curve Equation t Generators 12300d1 [0,-1,0,-1633,25762] 2 [-42:136:1]&[-23:225:1] 12300d2 [0,-1,0,-508,59512] 2 [-38:150:1]&[-18:250:1]
12300e (1 curve)	0	2- 3+ 5+ 41+	2- 3+ 5+ -4  3  4 -3  2
Curve Equation t 12300e1 [0,-1,0,-46770133,-123097296863] 1
12300f (1 curve)	1	2- 3+ 5+ 41-	2- 3+ 5+  2 -1  0  6  4
Curve Equation t Generators 12300f1 [0,-1,0,-333,2457] 1 [11:2:1]
12300g (2 curves)	1	2- 3+ 5+ 41-	2- 3+ 5+ -4 -4  0  0  4
Curve Equation t Generators 12300g1 [0,-1,0,-30033,-1992438] 2 [-99:27:1] 12300g2 [0,-1,0,-24908,-2699688] 2 [322:4750:1]
12300h (2 curves)	1	2- 3+ 5- 41+	2- 3+ 5-  4  0 -4  0  4
Curve Equation t Generators 12300h1 [0,-1,0,-630333,-192410838] 2 [-11055978798:-40418634:24137569] 12300h2 [0,-1,0,-629708,-192812088] 2 [12458801643019874:-607660013058266133:4709529362728]
12300i (2 curves)	2	2- 3+ 5- 41-	2- 3+ 5-  0 -6 -6 -6 -6
Curve Equation t Generators 12300i1 [0,-1,0,-53,102] 2 [-7:9:1]&[-3:15:1] 12300i2 [0,-1,0,172,552] 2 [-2:14:1]&[2:30:1]
12300j (1 curve)	0	2- 3+ 5- 41-	2- 3+ 5- -3  4 -5 -4 -1
Curve Equation t 12300j1 [0,-1,0,-3333,-80463] 1
12300k (1 curve)	0	2- 3- 5+ 41-	2- 3- 5+  2 -1  2  1 -4
Curve Equation t 12300k1 [0,1,0,-333,2463] 1
12300l (1 curve)	0	2- 3- 5+ 41-	2- 3- 5+  3  4  5  4 -1
Curve Equation t 12300l1 [0,1,0,-133,-697] 1
12300m (2 curves)	0	2- 3- 5+ 41-	2- 3- 5+ -4 -4 -4  4 -4
Curve Equation t 12300m1 [0,1,0,-9033,-331812] 2 12300m2 [0,1,0,-3908,-700812] 2
12300n (1 curve)	0	2- 3- 5- 41+	2- 3- 5-  4  0  2  3  8
Curve Equation t 12300n1 [0,1,0,67,63] 1
12300o (2 curves)	0	2- 3- 5- 41+	2- 3- 5- -4  0  4  0  4
Curve Equation t 12300o1 [0,1,0,-25213,-1549372] 2 12300o2 [0,1,0,-25188,-1552572] 2
12300p (2 curves)	1	2- 3- 5- 41-	2- 3- 5-  0 -6  6  6 -6
Curve Equation t Generators 12300p1 [0,1,0,-1333,10088] 2 [-28:162:1] 12300p2 [0,1,0,4292,77588] 2 [26:2421:8]
12300q (1 curve)	1	2- 3- 5- 41-	2- 3- 5- -2 -1  0 -6  4
Curve Equation t Generators 12300q1 [0,1,0,-8333,290463] 1 [58:75:1]

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

Part of Computational Number Theory
Back to Tables and computations