Elliptic curve search results

Results (21 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	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3990.bb6	3990bb6	3990.bb	3990bb	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( - 2 \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.55	2B	$31920$	$192$	$1$	$1$	$1$		$0$	$61440$	$1.880180$	$42502666283088696719/43898058864843750$	$0.99873$	$5.45086$	$[1, 0, 0, 72705, -6678225]$	\(y^2+xy=x^3+72705x-6678225\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.6, 24.48.0-24.bn.1.7, 152.48.0.?, $\ldots$	$[]$
11970.c6	11970r6	11970.c	11970r	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( - 2 \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.96	2B	$31920$	$192$	$1$	$1$	$1$		$0$	$491520$	$2.429485$	$42502666283088696719/43898058864843750$	$0.99873$	$5.51511$	$[1, -1, 0, 654345, 180312075]$	\(y^2+xy=x^3-x^2+654345x+180312075\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.8, 12.12.0-4.c.1.1, 24.48.0-24.bn.1.8, $\ldots$	$[]$
19950.o6	19950g6	19950.o	19950g	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2 \cdot 3^{3} \cdot 5^{14} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$1$		$0$	$1474560$	$2.684898$	$42502666283088696719/43898058864843750$	$0.99873$	$5.54013$	$[1, 1, 0, 1817625, -834778125]$	\(y^2+xy=x^3+x^2+1817625x-834778125\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 20.12.0-4.c.1.1, 24.24.0.bn.1, $\ldots$	$[]$
27930.ci6	27930cg5	27930.ci	27930cg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( - 2 \cdot 3^{3} \cdot 5^{8} \cdot 7^{14} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$2949120$	$2.853134$	$42502666283088696719/43898058864843750$	$0.99873$	$5.55524$	$[1, 1, 1, 3562544, 2294193719]$	\(y^2+xy+y=x^3+x^2+3562544x+2294193719\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 28.12.0-4.c.1.1, $\ldots$	$[]$
31920.ba6	31920bk5	31920.ba	31920bk	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{13} \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.45	2B	$31920$	$192$	$1$	$1.465890169$	$1$		$11$	$1474560$	$2.573326$	$42502666283088696719/43898058864843750$	$0.99873$	$5.15996$	$[0, -1, 0, 1163280, 427406400]$	\(y^2=x^3-x^2+1163280x+427406400\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 24.48.0-24.bn.1.5, 152.48.0.?, $\ldots$	$[(-160, 15400)]$
59850.fe6	59850fh5	59850.fe	59850fh	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2 \cdot 3^{9} \cdot 5^{14} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$1$		$0$	$11796480$	$3.234207$	$42502666283088696719/43898058864843750$	$0.99873$	$5.58606$	$[1, -1, 1, 16358620, 22555367997]$	\(y^2+xy+y=x^3-x^2+16358620x+22555367997\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 40.24.0-8.n.1.11, $\ldots$	$[]$
75810.x6	75810w5	75810.x	75810w	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19^{2} \)	\( - 2 \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.93	2B	$31920$	$192$	$1$	$8.275306991$	$1$		$0$	$22118400$	$3.352398$	$42502666283088696719/43898058864843750$	$0.99873$	$5.59477$	$[1, 1, 0, 26246498, 45858438274]$	\(y^2+xy=x^3+x^2+26246498x+45858438274\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.5, 24.48.0-24.bn.1.12, 76.12.0.?, $\ldots$	$[(188523/11, 399452011/11)]$
83790.bi6	83790cn5	83790.bi	83790cn	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( - 2 \cdot 3^{9} \cdot 5^{8} \cdot 7^{14} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$3.128369506$	$1$		$4$	$23592960$	$3.402443$	$42502666283088696719/43898058864843750$	$0.99873$	$5.59835$	$[1, -1, 0, 32062896, -61911167522]$	\(y^2+xy=x^3-x^2+32062896x-61911167522\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 56.24.0-8.n.1.12, $\ldots$	$[(3167, 265604)]$
95760.cu6	95760ea5	95760.cu	95760ea	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{13} \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.98	2B	$31920$	$192$	$1$	$3.953485272$	$1$		$3$	$11796480$	$3.122635$	$42502666283088696719/43898058864843750$	$0.99873$	$5.24042$	$[0, 0, 0, 10469517, -11550442318]$	\(y^2=x^3+10469517x-11550442318\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.4, 12.12.0-4.c.1.2, 24.48.0-24.bn.1.6, $\ldots$	$[(3506, 261250)]$
127680.d6	127680j5	127680.d	127680j	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{19} \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.95	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$1$	$11796480$	$2.919903$	$42502666283088696719/43898058864843750$	$0.99873$	$4.90528$	$[0, -1, 0, 4653119, -3423904319]$	\(y^2=x^3-x^2+4653119x-3423904319\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.9, 12.12.0-4.c.1.1, 24.48.0-24.bn.1.1, $\ldots$	$[]$
127680.ew6	127680fi5	127680.ew	127680fi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{19} \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.97	2B	$31920$	$192$	$1$	$1$	$1$		$1$	$11796480$	$2.919903$	$42502666283088696719/43898058864843750$	$0.99873$	$4.90528$	$[0, 1, 0, 4653119, 3423904319]$	\(y^2=x^3+x^2+4653119x+3423904319\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.11, 12.12.0-4.c.1.2, 24.48.0-24.bn.1.3, $\ldots$	$[]$
139650.ef6	139650ha6	139650.ef	139650ha	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( - 2 \cdot 3^{3} \cdot 5^{14} \cdot 7^{14} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.3	2B	$31920$	$192$	$1$	$1$	$4$	$2$	$0$	$70778880$	$3.657856$	$42502666283088696719/43898058864843750$	$0.99873$	$5.61566$	$[1, 0, 1, 89063599, 286596087698]$	\(y^2+xy+y=x^3+89063599x+286596087698\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.5, 24.24.0.bn.1, $\ldots$	$[]$
159600.do6	159600bt6	159600.do	159600bt	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{13} \cdot 3^{3} \cdot 5^{14} \cdot 7^{8} \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$10.90968063$	$1$		$11$	$35389440$	$3.378048$	$42502666283088696719/43898058864843750$	$0.99873$	$5.27281$	$[0, 1, 0, 29081992, 53483963988]$	\(y^2=x^3+x^2+29081992x+53483963988\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 20.12.0-4.c.1.2, 24.24.0.bn.1, $\ldots$	$[(724, 273714), (19932, 2924418)]$
223440.dt6	223440bv5	223440.dt	223440bv	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( - 2^{13} \cdot 3^{3} \cdot 5^{8} \cdot 7^{14} \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$8.340871073$	$1$		$17$	$70778880$	$3.546284$	$42502666283088696719/43898058864843750$	$0.99873$	$5.29267$	$[0, 1, 0, 57000704, -146714396620]$	\(y^2=x^3+x^2+57000704x-146714396620\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 28.12.0-4.c.1.2, $\ldots$	$[(6722, 735000), (2972, 221250)]$
227430.dg6	227430bq5	227430.dg	227430bq	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19^{2} \)	\( - 2 \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.89	2B	$31920$	$192$	$1$	$1$	$16$	$2$	$0$	$176947200$	$3.901707$	$42502666283088696719/43898058864843750$	$0.99873$	$5.63086$	$[1, -1, 1, 236218477, -1237941614919]$	\(y^2+xy+y=x^3-x^2+236218477x-1237941614919\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 24.48.0-24.bn.1.11, 152.48.0.?, $\ldots$	$[]$
379050.kd6	379050kd6	379050.kd	379050kd	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19^{2} \)	\( - 2 \cdot 3^{3} \cdot 5^{14} \cdot 7^{8} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$18.22960780$	$1$		$0$	$530841600$	$4.157120$	$42502666283088696719/43898058864843750$	$0.99873$	$5.64554$	$[1, 0, 0, 656162437, 5730992459367]$	\(y^2+xy=x^3+656162437x+5730992459367\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 40.24.0-8.n.1.4, $\ldots$	$[(-4530392453/854, 742908144046181/854)]$
383040.ki6	383040ki6	383040.ki	383040ki	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{19} \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.56	2B	$31920$	$192$	$1$	$1$	$1$		$1$	$94371840$	$3.469208$	$42502666283088696719/43898058864843750$	$0.99873$	$4.99883$	$[0, 0, 0, 41878068, 92403538544]$	\(y^2=x^3+41878068x+92403538544\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 24.48.0-24.bn.1.2, 152.48.0.?, $\ldots$	$[]$
383040.lp6	383040lp5	383040.lp	383040lp	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( - 2^{19} \cdot 3^{9} \cdot 5^{8} \cdot 7^{8} \cdot 19^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.46	2B	$31920$	$192$	$1$	$1.027075227$	$1$		$17$	$94371840$	$3.469208$	$42502666283088696719/43898058864843750$	$0.99873$	$4.99883$	$[0, 0, 0, 41878068, -92403538544]$	\(y^2=x^3+41878068x-92403538544\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 24.48.0-24.bn.1.4, 152.48.0.?, $\ldots$	$[(2642, 191520)]$
418950.ko6	418950ko5	418950.ko	418950ko	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( - 2 \cdot 3^{9} \cdot 5^{14} \cdot 7^{14} \cdot 19^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$31920$	$192$	$1$	$21.15018093$	$1$		$0$	$566231040$	$4.207161$	$42502666283088696719/43898058864843750$	$0.99873$	$5.64828$	$[1, -1, 1, 801572395, -7738094367853]$	\(y^2+xy+y=x^3-x^2+801572395x-7738094367853\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.6, 24.24.0.bn.1, $\ldots$	$[(411943249479/3034, 302440118170974955/3034)]$
478800.gk6	478800gk5	478800.gk	478800gk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( - 2^{13} \cdot 3^{9} \cdot 5^{14} \cdot 7^{8} \cdot 19^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$31920$	$192$	$1$	$1$	$1$		$1$	$283115520$	$3.927353$	$42502666283088696719/43898058864843750$	$0.99873$	$5.33389$	$[0, 0, 0, 261737925, -1443805289750]$	\(y^2=x^3+261737925x-1443805289750\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 40.24.0-8.n.1.9, $\ldots$	$[]$
482790.dr6	482790dr6	482790.dr	482790dr	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( - 2 \cdot 3^{3} \cdot 5^{8} \cdot 7^{8} \cdot 11^{6} \cdot 19^{2} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$351120$	$192$	$1$	$0.586017040$	$1$		$22$	$78643200$	$3.079128$	$42502666283088696719/43898058864843750$	$0.99873$	$4.55276$	$[1, 0, 1, 8797302, 8897514778]$	\(y^2+xy+y=x^3+8797302x+8897514778\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bn.1, 44.12.0-4.c.1.1, $\ldots$	$[(1484, 158070), (-166, 86295)]$