Cremona's table of elliptic curves

83824 = 2⁴ · 13² · 31

Class	r	Atkin-Lehner	Eigenvalues
83824a (1 curve)	1	2+ 13+ 31+	2+ -1 -1 -3  4 13+  3 -2
Curve Equation t Generators 83824a1 [0,-1,0,-196096,-34073248] 1 [2674:136214:1]
83824b (1 curve)	1	2+ 13+ 31+	2+  2 -1 -3 -2 13+ -6  1
Curve Equation t Generators 83824b1 [0,-1,0,-56,-2341] 1 [5781:84331:27]
83824c (2 curves)	1	2+ 13+ 31+	2+  2 -2  0  2 13+  6  4
Curve Equation t Generators 83824c1 [0,-1,0,1296,5264] 2 [190274:4486950:343] 83824c2 [0,-1,0,-5464,48528] 2 [-72:252:1]
83824d (1 curve)	1	2+ 13+ 31+	2+ -3  2  5 -3 13+  5  5
Curve Equation t Generators 83824d1 [0,0,0,-15379,714025] 1 [0:845:1]
83824e (1 curve)	0	2+ 13+ 31-	2+  0  3 -3  2 13+  0  1
Curve Equation t 83824e1 [0,0,0,169,2197] 1
83824f (1 curve)	0	2+ 13+ 31-	2+  0  4 -2  3 13+  8  4
Curve Equation t 83824f1 [0,0,0,-15548,-746980] 1
83824g (1 curve)	0	2+ 13+ 31-	2+  2  1 -1 -2 13+  0  7
Curve Equation t 83824g1 [0,-1,0,-90640,10576383] 1
83824h (1 curve)	2	2+ 13+ 31-	2+ -3 -2 -5  3 13+  5 -5
Curve Equation t Generators 83824h1 [0,0,0,-91,325] 1 [12:31:1]&[4:5:1]
83824i (1 curve)	0	2+ 13+ 31-	2+ -3  3  3  2 13+  3  4
Curve Equation t 83824i1 [0,0,0,-23491,7087522] 1
83824j (1 curve)	0	2- 13+ 31+	2-  0 -1  3  6 13+  0 -5
Curve Equation t 83824j1 [0,0,0,-2873,59319] 1
83824k (4 curves)	0	2- 13+ 31+	2-  0  2  0  0 13+ -6  4
Curve Equation t 83824k1 [0,0,0,-1859,-153790] 2 83824k2 [0,0,0,-55939,-5075070] 4 83824k3 [0,0,0,-82979,338338] 2 83824k4 [0,0,0,-894179,-325450398] 2
83824l (1 curve)	0	2- 13+ 31+	2-  0  3  2  0 13+  5  4
Curve Equation t 83824l1 [0,0,0,-314171,-76486358] 1
83824m (1 curve)	0	2- 13+ 31+	2-  0  4 -2  1 13+  0  0
Curve Equation t 83824m1 [0,0,0,-45968,-177913060] 1
83824n (1 curve)	0	2- 13+ 31+	2-  1  1  1  2 13+  7 -4
Curve Equation t 83824n1 [0,1,0,139200,27819572] 1
83824o (1 curve)	2	2- 13+ 31+	2-  1 -2  0  1 13+  0 -6
Curve Equation t Generators 83824o1 [0,1,0,1296,27860] 1 [82:832:1]&[268:4438:1]
83824p (1 curve)	0	2- 13+ 31+	2-  1 -2  1 -1 13+  7  5
Curve Equation t 83824p1 [0,1,0,-394,-1949] 1
83824q (1 curve)	2	2- 13+ 31+	2- -1 -1 -3  0 13+ -5 -2
Curve Equation t Generators 83824q1 [0,-1,0,-6816,-4280576] 1 [490:10478:1]&[178:338:1]
83824r (1 curve)	0	2- 13+ 31+	2- -1  3 -3 -4 13+  3 -4
Curve Equation t 83824r1 [0,-1,0,-262344,-51808784] 1
83824s (1 curve)	2	2- 13+ 31+	2- -1 -4  0 -3 13+ -2 -2
Curve Equation t Generators 83824s1 [0,-1,0,-160,896] 1 [8:8:1]&[-8:40:1]
83824t (1 curve)	0	2- 13+ 31+	2-  2 -3 -3  2 13+  0 -7
Curve Equation t 83824t1 [0,-1,0,958,28079] 1
83824u (1 curve)	0	2- 13+ 31+	2- -2  1  1  2 13+  4  5
Curve Equation t 83824u1 [0,1,0,-156550,23789091] 1
83824v (1 curve)	0	2- 13+ 31+	2-  3 -1 -3  0 13+  3 -8
Curve Equation t 83824v1 [0,0,0,860717,321592466] 1
83824w (1 curve)	1	2- 13+ 31-	2-  0 -3 -2  0 13+  5 -4
Curve Equation t Generators 83824w1 [0,0,0,-1859,-34814] 1 [79:558:1]
83824x (2 curves)	1	2- 13+ 31-	2-  1 -1  3  2 13+  3  0
Curve Equation t Generators 83824x1 [0,1,0,-38139976,-90676227212] 1 [5376654293526:-42342158111968:751089429] 83824x2 [0,1,0,180856984,-314382852172] 1 [73882566:23723407448:729]
83824y (1 curve)	1	2- 13+ 31-	2-  1  2  0 -1 13+  0  6
Curve Equation t Generators 83824y1 [0,1,0,218968,60332468] 1 [188915339946366:34521431798931013:5658783768]
83824z (1 curve)	1	2- 13+ 31-	2-  1  2 -1  1 13+  7 -5
Curve Equation t Generators 83824z1 [0,1,0,-66642,-4015465] 1 [-45304:560015:512]
83824ba (3 curves)	1	2- 13+ 31-	2- -1 -3 -1  0 13+  3  2
Curve Equation t Generators 83824ba1 [0,-1,0,6789688,-5512936976] 1 [3361260:343343104:343] 83824ba2 [0,-1,0,-69354952,308424491504] 1 [-2188:670592:1] 83824ba3 [0,-1,0,-6201918792,187993150154224] 1 [42948:922064:1]
83824bb (1 curve)	1	2- 13+ 31-	2- -1  4  0  3 13+ -2  2
Curve Equation t Generators 83824bb1 [0,-1,0,-27096,1860208] 1 [-1014:14405:8]
83824bc (2 curves)	1	2- 13+ 31-	2-  2  3 -1 -6 13+  6 -1
Curve Equation t Generators 83824bc1 [0,-1,0,-394,-3693] 1 [58984335:19874231:2460375] 83824bc2 [0,-1,0,2986,36191] 1 [-8415:5239:729]
83824bd (1 curve)	1	2- 13+ 31-	2- -2 -1  3  2 13+  6  3
Curve Equation t Generators 83824bd1 [0,1,0,-11886,634063] 1 [-87:22139:27]
83824be (1 curve)	1	2- 13- 31+	2-  1 -1 -1  2 13- -1 -2
Curve Equation t Generators 83824be1 [0,1,0,-3718056,-2760826444] 1 [3413300:90037454:1331]
83824bf (1 curve)	1	2- 13- 31+	2-  1 -1  5 -4 13- -7 -2
Curve Equation t Generators 83824bf1 [0,1,0,-26056,3522676] 1 [30:-1664:1]
83824bg (1 curve)	1	2- 13- 31+	2- -2 -4  2 -1 13-  2 -2
Curve Equation t Generators 83824bg1 [0,1,0,23435,1107939] 1 [9668:182351:64]
83824bh (1 curve)	0	2- 13- 31-	2-  1  1  1 -2 13- -1  2
Curve Equation t 83824bh1 [0,1,0,-22000,-1263404] 1
83824bi (1 curve)	0	2- 13- 31-	2-  1  1 -5  4 13- -7  2
Curve Equation t 83824bi1 [0,1,0,-4403520,7756933172] 1
83824bj (1 curve)	0	2- 13- 31-	2- -2  4 -2  1 13-  2  2
Curve Equation t 83824bj1 [0,1,0,139,547] 1

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

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