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.k2	8470c2	8470.k	8470c	$2$	$3$	\( 2 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 5^{6} \cdot 7^{3} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$114048$	$2.030602$	$3639707951/10718750$	$[1, 0, 1, 94861, -22731788]$	\(y^2+xy+y=x^3+94861x-22731788\)
8470.bd2	8470x2	8470.bd	8470x	$2$	$3$	\( 2 \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 5^{6} \cdot 7^{3} \cdot 11^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$10368$	$0.831655$	$3639707951/10718750$	$[1, 0, 0, 784, 17150]$	\(y^2+xy=x^3+784x+17150\)
42350.h2	42350j2	42350.h	42350j	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$4.199312801$	$1$		$8$	$248832$	$1.636374$	$3639707951/10718750$	$[1, 1, 0, 19600, 2143750]$	\(y^2+xy=x^3+x^2+19600x+2143750\)
42350.cc2	42350cl2	42350.cc	42350cl	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$4$	$2$	$0$	$2737152$	$2.835320$	$3639707951/10718750$	$[1, 1, 1, 2371537, -2841473469]$	\(y^2+xy+y=x^3+x^2+2371537x-2841473469\)
59290.x2	59290by2	59290.x	59290by	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2 \cdot 5^{6} \cdot 7^{9} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$5474304$	$3.003555$	$3639707951/10718750$	$[1, 1, 0, 4648213, 7801651411]$	\(y^2+xy=x^3+x^2+4648213x+7801651411\)
59290.db2	59290em2	59290.db	59290em	$2$	$3$	\( 2 \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2 \cdot 5^{6} \cdot 7^{9} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.879131867$	$1$		$0$	$497664$	$1.804609$	$3639707951/10718750$	$[1, 1, 1, 38415, -5844035]$	\(y^2+xy+y=x^3+x^2+38415x-5844035\)
67760.i2	67760bd2	67760.i	67760bd	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{6} \cdot 7^{3} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.751483987$	$1$		$4$	$248832$	$1.524801$	$3639707951/10718750$	$[0, -1, 0, 12544, -1097600]$	\(y^2=x^3-x^2+12544x-1097600\)
67760.j2	67760bp2	67760.j	67760bp	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{6} \cdot 7^{3} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$2737152$	$2.723751$	$3639707951/10718750$	$[0, -1, 0, 1517784, 1454834416]$	\(y^2=x^3-x^2+1517784x+1454834416\)
76230.cq2	76230cp2	76230.cq	76230cp	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 3^{6} \cdot 5^{6} \cdot 7^{3} \cdot 11^{4} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$3.231895829$	$1$		$4$	$311040$	$1.380960$	$3639707951/10718750$	$[1, -1, 0, 7056, -463050]$	\(y^2+xy=x^3-x^2+7056x-463050\)
76230.dw2	76230eq2	76230.dw	76230eq	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 3^{6} \cdot 5^{6} \cdot 7^{3} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$13.37379189$	$1$		$0$	$3421440$	$2.579906$	$3639707951/10718750$	$[1, -1, 1, 853753, 613758269]$	\(y^2+xy+y=x^3-x^2+853753x+613758269\)
271040.cm2	271040cm2	271040.cm	271040cm	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{19} \cdot 5^{6} \cdot 7^{3} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$8.068427772$	$1$		$2$	$21897216$	$3.070324$	$3639707951/10718750$	$[0, -1, 0, 6071135, -11644746463]$	\(y^2=x^3-x^2+6071135x-11644746463\)
271040.co2	271040co2	271040.co	271040co	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{19} \cdot 5^{6} \cdot 7^{3} \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.231914871$	$1$		$24$	$1990656$	$1.871376$	$3639707951/10718750$	$[0, -1, 0, 50175, 8730625]$	\(y^2=x^3-x^2+50175x+8730625\)
271040.fh2	271040fh2	271040.fh	271040fh	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{19} \cdot 5^{6} \cdot 7^{3} \cdot 11^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$1990656$	$1.871376$	$3639707951/10718750$	$[0, 1, 0, 50175, -8730625]$	\(y^2=x^3+x^2+50175x-8730625\)
271040.fv2	271040fv2	271040.fv	271040fv	$2$	$3$	\( 2^{6} \cdot 5 \cdot 7 \cdot 11^{2} \)	\( - 2^{19} \cdot 5^{6} \cdot 7^{3} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3.807716643$	$1$		$2$	$21897216$	$3.070324$	$3639707951/10718750$	$[0, 1, 0, 6071135, 11644746463]$	\(y^2=x^3+x^2+6071135x+11644746463\)
296450.ei2	296450ei2	296450.ei	296450ei	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 2 \cdot 5^{12} \cdot 7^{9} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$5.171163593$	$1$		$0$	$11943936$	$2.609329$	$3639707951/10718750$	$[1, 0, 1, 960374, -732425102]$	\(y^2+xy+y=x^3+960374x-732425102\)
296450.iz2	296450iz2	296450.iz	296450iz	$2$	$3$	\( 2 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 2 \cdot 5^{12} \cdot 7^{9} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$9$	$3$	$0$	$131383296$	$3.808277$	$3639707951/10718750$	$[1, 0, 0, 116205312, 974974015742]$	\(y^2+xy=x^3+116205312x+974974015742\)
338800.gi2	338800gi2	338800.gi	338800gi	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$13.88762595$	$1$		$0$	$65691648$	$3.528469$	$3639707951/10718750$	$[0, 1, 0, 37944592, 181930191188]$	\(y^2=x^3+x^2+37944592x+181930191188\)
338800.gk2	338800gk2	338800.gk	338800gk	$2$	$3$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.021102834$	$1$		$10$	$5971968$	$2.329521$	$3639707951/10718750$	$[0, 1, 0, 313592, -136572812]$	\(y^2=x^3+x^2+313592x-136572812\)
381150.hx2	381150hx2	381150.hx	381150hx	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 3^{6} \cdot 5^{12} \cdot 7^{3} \cdot 11^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$82114560$	$3.384628$	$3639707951/10718750$	$[1, -1, 0, 21343833, 76741127491]$	\(y^2+xy=x^3-x^2+21343833x+76741127491\)
381150.ja2	381150ja2	381150.ja	381150ja	$2$	$3$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11^{2} \)	\( - 2 \cdot 3^{6} \cdot 5^{12} \cdot 7^{3} \cdot 11^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$7464960$	$2.185680$	$3639707951/10718750$	$[1, -1, 1, 176395, -57704853]$	\(y^2+xy+y=x^3-x^2+176395x-57704853\)
474320.hd2	474320hd2	474320.hd	474320hd	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{6} \cdot 7^{9} \cdot 11^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.204546656$	$1$		$6$	$11943936$	$2.497757$	$3639707951/10718750$	$[0, 1, 0, 614640, 375247508]$	\(y^2=x^3+x^2+614640x+375247508\)
474320.ia2	474320ia2	474320.ia	474320ia	$2$	$3$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 11^{2} \)	\( - 2^{13} \cdot 5^{6} \cdot 7^{9} \cdot 11^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$16.61298875$	$1$		$0$	$131383296$	$3.696705$	$3639707951/10718750$	$[0, 1, 0, 74371400, -499156947500]$	\(y^2=x^3+x^2+74371400x-499156947500\)