Elliptic curves over $\Q$ of conductor 1850

Results (28 matches)

 

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
1850.a1	1850g1	1850.a	1850g	$2$	$3$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{10} \cdot 5^{4} \cdot 37^{3} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$0.677837982$	$1$		$8$	$1800$	$0.704188$	$-19026212425/51868672$	$[1, 0, 1, -476, 9498]$	\(y^2+xy+y=x^3-476x+9498\)
1850.a2	1850g2	1850.a	1850g	$2$	$3$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{30} \cdot 5^{4} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$2.033513947$	$1$		$0$	$5400$	$1.253494$	$12642252501575/39728447488$	$[1, 0, 1, 4149, -216202]$	\(y^2+xy+y=x^3+4149x-216202\)
1850.b1	1850b1	1850.b	1850b	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{6} \cdot 5^{2} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.507639273$	$1$		$4$	$216$	$-0.405339$	$-625/2368$	$[1, 0, 1, -1, -12]$	\(y^2+xy+y=x^3-x-12\)
1850.c1	1850c1	1850.c	1850c	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2 \cdot 5^{8} \cdot 37^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$1$	$1$		$0$	$960$	$0.413319$	$-121945/2738$	$[1, 1, 0, -75, -1625]$	\(y^2+xy=x^3+x^2-75x-1625\)
1850.d1	1850e1	1850.d	1850e	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{3} \cdot 5^{9} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.686718092$	$1$		$4$	$720$	$0.391537$	$-804357/296$	$[1, -1, 0, -242, 1916]$	\(y^2+xy=x^3-x^2-242x+1916\)
1850.e1	1850f2	1850.e	1850f	$2$	$2$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{9} \cdot 5^{3} \cdot 37^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.115691247$	$1$		$2$	$1728$	$0.886325$	$2253707317528029/700928$	$[1, -1, 0, -13657, -610899]$	\(y^2+xy=x^3-x^2-13657x-610899\)
1850.e2	1850f1	1850.e	1850f	$2$	$2$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{18} \cdot 5^{3} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.557845623$	$1$		$3$	$864$	$0.539751$	$557238592989/9699328$	$[1, -1, 0, -857, -9299]$	\(y^2+xy=x^3-x^2-857x-9299\)
1850.f1	1850a3	1850.f	1850a	$4$	$6$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{4} \cdot 5^{7} \cdot 37^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$11.27996712$	$1$		$1$	$6912$	$1.448227$	$16232905099479601/4052240$	$[1, 1, 0, -131875, -18487875]$	\(y^2+xy=x^3+x^2-131875x-18487875\)
1850.f2	1850a4	1850.f	1850a	$4$	$6$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{2} \cdot 5^{8} \cdot 37^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$5.639983561$	$1$		$2$	$13824$	$1.794800$	$-16048965315233521/256572640900$	$[1, 1, 0, -131375, -18634375]$	\(y^2+xy=x^3+x^2-131375x-18634375\)
1850.f3	1850a1	1850.f	1850a	$4$	$6$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{12} \cdot 5^{9} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.3, 3.4.0.1	2B, 3B	$3.759989040$	$1$		$3$	$2304$	$0.898921$	$46694890801/18944000$	$[1, 1, 0, -1875, -17875]$	\(y^2+xy=x^3+x^2-1875x-17875\)
1850.f4	1850a2	1850.f	1850a	$4$	$6$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{6} \cdot 5^{12} \cdot 37^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	4.6.0.5, 3.4.0.1	2B, 3B	$1.879994520$	$1$		$2$	$4608$	$1.245495$	$1625964918479/1369000000$	$[1, 1, 0, 6125, -121875]$	\(y^2+xy=x^3+x^2+6125x-121875\)
1850.g1	1850d1	1850.g	1850d	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{23} \cdot 5^{8} \cdot 37^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$1$	$1$		$0$	$22080$	$1.747602$	$-132384574175625/11484004352$	$[1, -1, 0, -77617, 8944541]$	\(y^2+xy=x^3-x^2-77617x+8944541\)
1850.h1	1850m1	1850.h	1850m	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{23} \cdot 5^{2} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$0.062324207$	$1$		$10$	$4416$	$0.942883$	$-132384574175625/11484004352$	$[1, -1, 1, -3105, 72177]$	\(y^2+xy+y=x^3-x^2-3105x+72177\)
1850.i1	1850l1	1850.i	1850l	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{11} \cdot 5^{7} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.100155033$	$1$		$12$	$1056$	$0.559989$	$214921799/378880$	$[1, 0, 0, 312, -3008]$	\(y^2+xy=x^3+312x-3008\)
1850.j1	1850o2	1850.j	1850o	$2$	$2$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{9} \cdot 5^{9} \cdot 37^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.217067129$	$1$		$4$	$8640$	$1.691044$	$2253707317528029/700928$	$[1, -1, 1, -341430, -76703803]$	\(y^2+xy+y=x^3-x^2-341430x-76703803\)
1850.j2	1850o1	1850.j	1850o	$2$	$2$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{18} \cdot 5^{9} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.108533564$	$1$		$7$	$4320$	$1.344471$	$557238592989/9699328$	$[1, -1, 1, -21430, -1183803]$	\(y^2+xy+y=x^3-x^2-21430x-1183803\)
1850.k1	1850j3	1850.k	1850j	$4$	$4$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2 \cdot 5^{10} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$8.348155895$	$1$		$0$	$1536$	$0.881229$	$6825481747209/46250$	$[1, -1, 1, -9880, -375503]$	\(y^2+xy+y=x^3-x^2-9880x-375503\)
1850.k2	1850j2	1850.k	1850j	$4$	$4$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{2} \cdot 5^{8} \cdot 37^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$4.174077947$	$1$		$2$	$768$	$0.534657$	$1767172329/136900$	$[1, -1, 1, -630, -5503]$	\(y^2+xy+y=x^3-x^2-630x-5503\)
1850.k3	1850j1	1850.k	1850j	$4$	$4$	\( 2 \cdot 5^{2} \cdot 37 \)	\( 2^{4} \cdot 5^{7} \cdot 37 \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$2.087038973$	$1$		$7$	$384$	$0.188082$	$15438249/2960$	$[1, -1, 1, -130, 497]$	\(y^2+xy+y=x^3-x^2-130x+497\)
1850.k4	1850j4	1850.k	1850j	$4$	$4$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2 \cdot 5^{7} \cdot 37^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$2.087038973$	$1$		$0$	$1536$	$0.881229$	$1689410871/18741610$	$[1, -1, 1, 620, -25503]$	\(y^2+xy+y=x^3-x^2+620x-25503\)
1850.l1	1850n1	1850.l	1850n	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{3} \cdot 5^{3} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$0.196247114$	$1$		$6$	$144$	$-0.413182$	$-804357/296$	$[1, -1, 1, -10, 17]$	\(y^2+xy+y=x^3-x^2-10x+17\)
1850.m1	1850k1	1850.m	1850k	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2 \cdot 5^{2} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2$	8.2.0.1		$1.449379421$	$1$		$0$	$192$	$-0.391400$	$-121945/2738$	$[1, 0, 0, -3, -13]$	\(y^2+xy=x^3-3x-13\)
1850.n1	1850p1	1850.n	1850p	$1$	$1$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{6} \cdot 5^{8} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1$	$1$		$0$	$1080$	$0.399380$	$-625/2368$	$[1, 1, 1, -13, -1469]$	\(y^2+xy+y=x^3+x^2-13x-1469\)
1850.o1	1850h1	1850.o	1850h	$3$	$9$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2 \cdot 5^{7} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$864$	$0.413506$	$-16954786009/370$	$[1, 1, 1, -1338, 18281]$	\(y^2+xy+y=x^3+x^2-1338x+18281\)
1850.o2	1850h2	1850.o	1850h	$3$	$9$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{3} \cdot 5^{9} \cdot 37^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.12.0.1	3Cs	$1$	$1$		$0$	$2592$	$0.962812$	$-702595369/50653000$	$[1, 1, 1, -463, 42781]$	\(y^2+xy+y=x^3+x^2-463x+42781\)
1850.o3	1850h3	1850.o	1850h	$3$	$9$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{9} \cdot 5^{15} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.12.0.1	3B	$1$	$1$		$0$	$7776$	$1.512117$	$510273943271/37000000000$	$[1, 1, 1, 4162, -1150469]$	\(y^2+xy+y=x^3+x^2+4162x-1150469\)
1850.p1	1850i1	1850.p	1850i	$2$	$3$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{10} \cdot 5^{10} \cdot 37^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$9000$	$1.508907$	$-19026212425/51868672$	$[1, 1, 1, -11888, 1187281]$	\(y^2+xy+y=x^3+x^2-11888x+1187281\)
1850.p2	1850i2	1850.p	1850i	$2$	$3$	\( 2 \cdot 5^{2} \cdot 37 \)	\( - 2^{30} \cdot 5^{10} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$27000$	$2.058212$	$12642252501575/39728447488$	$[1, 1, 1, 103737, -27025219]$	\(y^2+xy+y=x^3+x^2+103737x-27025219\)