Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (22 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
8470.k1	8470c1	8470.k	8470c	$2$	$3$	\( 2 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{2} \cdot 7 \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$38016$	$1.481297$	$-584043889/1400$	$[1, 0, 1, -51549, -4518384]$	\(y^2+xy+y=x^3-51549x-4518384\)
8470.bd1	8470x1	8470.bd	8470x	$2$	$3$	\( 2 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{2} \cdot 7 \cdot 11^{4} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$1$	$1$		$2$	$3456$	$0.282348$	$-584043889/1400$	$[1, 0, 0, -426, 3356]$	\(y^2+xy=x^3-426x+3356\)
42350.h1	42350j1	42350.h	42350j	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{8} \cdot 7 \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.466590311$	$1$		$12$	$82944$	$1.087067$	$-584043889/1400$	$[1, 1, 0, -10650, 419500]$	\(y^2+xy=x^3+x^2-10650x+419500\)
42350.cc1	42350cl1	42350.cc	42350cl	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{8} \cdot 7 \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$4$	$2$	$0$	$912384$	$2.286015$	$-584043889/1400$	$[1, 1, 1, -1288713, -564797969]$	\(y^2+xy+y=x^3+x^2-1288713x-564797969\)
59290.x1	59290by1	59290.x	59290by	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$1824768$	$2.454250$	$-584043889/1400$	$[1, 1, 0, -2525877, 1547279749]$	\(y^2+xy=x^3+x^2-2525877x+1547279749\)
59290.db1	59290em1	59290.db	59290em	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{2} \cdot 7^{7} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.959710622$	$1$		$4$	$165888$	$1.255302$	$-584043889/1400$	$[1, 1, 1, -20875, -1171983]$	\(y^2+xy+y=x^3+x^2-20875x-1171983\)
67760.i1	67760bd1	67760.i	67760bd	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{2} \cdot 7 \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.254451962$	$1$		$4$	$82944$	$0.975495$	$-584043889/1400$	$[0, -1, 0, -6816, -214784]$	\(y^2=x^3-x^2-6816x-214784\)
67760.j1	67760bp1	67760.j	67760bp	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{2} \cdot 7 \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$912384$	$2.174442$	$-584043889/1400$	$[0, -1, 0, -824776, 289176560]$	\(y^2=x^3-x^2-824776x+289176560\)
76230.cq1	76230cp1	76230.cq	76230cp	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$9.695687487$	$1$		$0$	$103680$	$0.831655$	$-584043889/1400$	$[1, -1, 0, -3834, -90612]$	\(y^2+xy=x^3-x^2-3834x-90612\)
76230.dw1	76230eq1	76230.dw	76230eq	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4.457930631$	$1$		$2$	$1140480$	$2.030602$	$-584043889/1400$	$[1, -1, 1, -463937, 121996361]$	\(y^2+xy+y=x^3-x^2-463937x+121996361\)
271040.cm1	271040cm1	271040.cm	271040cm	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{21} \cdot 5^{2} \cdot 7 \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$24.20528331$	$1$		$0$	$7299072$	$2.521015$	$-584043889/1400$	$[0, -1, 0, -3299105, -2310113375]$	\(y^2=x^3-x^2-3299105x-2310113375\)
271040.co1	271040co1	271040.co	271040co	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{21} \cdot 5^{2} \cdot 7 \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.087233844$	$1$		$10$	$663552$	$1.322069$	$-584043889/1400$	$[0, -1, 0, -27265, 1745537]$	\(y^2=x^3-x^2-27265x+1745537\)
271040.fh1	271040fh1	271040.fh	271040fh	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{21} \cdot 5^{2} \cdot 7 \cdot 11^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$663552$	$1.322069$	$-584043889/1400$	$[0, 1, 0, -27265, -1745537]$	\(y^2=x^3+x^2-27265x-1745537\)
271040.fv1	271040fv1	271040.fv	271040fv	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{21} \cdot 5^{2} \cdot 7 \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$11.42314993$	$1$		$0$	$7299072$	$2.521015$	$-584043889/1400$	$[0, 1, 0, -3299105, 2310113375]$	\(y^2=x^3+x^2-3299105x+2310113375\)
296450.ei1	296450ei1	296450.ei	296450ei	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{8} \cdot 7^{7} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.723721197$	$1$		$2$	$3981312$	$2.060020$	$-584043889/1400$	$[1, 0, 1, -521876, -145454102]$	\(y^2+xy+y=x^3-521876x-145454102\)
296450.iz1	296450iz1	296450.iz	296450iz	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{3} \cdot 5^{8} \cdot 7^{7} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$43794432$	$3.258968$	$-584043889/1400$	$[1, 0, 0, -63146938, 193536262492]$	\(y^2+xy=x^3-63146938x+193536262492\)
338800.gi1	338800gi1	338800.gi	338800gi	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{8} \cdot 7 \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4.629208652$	$1$		$2$	$21897216$	$2.979160$	$-584043889/1400$	$[0, 1, 0, -20619408, 36105831188]$	\(y^2=x^3+x^2-20619408x+36105831188\)
338800.gk1	338800gk1	338800.gk	338800gk	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{8} \cdot 7 \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$18.18992551$	$1$		$4$	$1990656$	$1.780214$	$-584043889/1400$	$[0, 1, 0, -170408, -27188812]$	\(y^2=x^3+x^2-170408x-27188812\)
381150.hx1	381150hx1	381150.hx	381150hx	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{6} \cdot 5^{8} \cdot 7 \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$27371520$	$2.835320$	$-584043889/1400$	$[1, -1, 0, -11598417, 15237946741]$	\(y^2+xy=x^3-x^2-11598417x+15237946741\)
381150.ja1	381150ja1	381150.ja	381150ja	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{3} \cdot 3^{6} \cdot 5^{8} \cdot 7 \cdot 11^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$2488320$	$1.636374$	$-584043889/1400$	$[1, -1, 1, -95855, -11422353]$	\(y^2+xy+y=x^3-x^2-95855x-11422353\)
474320.hd1	474320hd1	474320.hd	474320hd	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{2} \cdot 7^{7} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.613639968$	$1$		$4$	$3981312$	$1.948450$	$-584043889/1400$	$[0, 1, 0, -334000, 74338900]$	\(y^2=x^3+x^2-334000x+74338900\)
474320.ia1	474320ia1	474320.ia	474320ia	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{15} \cdot 5^{2} \cdot 7^{7} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$49.83896625$	$1$		$0$	$43794432$	$3.147400$	$-584043889/1400$	$[0, 1, 0, -40414040, -99106732012]$	\(y^2=x^3+x^2-40414040x-99106732012\)