Elliptic curves over $\Q$ of conductor 4335

Results (16 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
4335.a1	4335b1	4335.a	4335b	$1$	$1$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{6} \cdot 5^{7} \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$102816$	$2.066891$	$100471803904/56953125$	$1.08007$	$5.73156$	$[0, -1, 1, -185056, -4322394]$	\(y^2+y=x^3-x^2-185056x-4322394\)	10.2.0.a.1	$[]$
4335.b1	4335g1	4335.b	4335g	$1$	$1$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{6} \cdot 5^{7} \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.048859451$	$1$		$14$	$6048$	$0.650283$	$100471803904/56953125$	$1.08007$	$3.70167$	$[0, 1, 1, -640, -1106]$	\(y^2+y=x^3+x^2-640x-1106\)	10.2.0.a.1	$[(-4, 37)]$
4335.c1	4335d7	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$8160$	$768$	$13$	$1$	$4$	$2$	$0$	$20480$	$1.707476$	$1114544804970241/405$	$1.07354$	$6.16713$	$[1, 0, 0, -624246, -189889425]$	\(y^2+xy=x^3-624246x-189889425\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$	$[]$
4335.c2	4335d5	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 17^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$4080$	$768$	$13$	$1$	$1$		$2$	$10240$	$1.360903$	$272223782641/164025$	$1.03897$	$5.17396$	$[1, 0, 0, -39021, -2968560]$	\(y^2+xy=x^3-39021x-2968560\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$	$[]$
4335.c3	4335d8	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( - 3^{16} \cdot 5 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$8160$	$768$	$13$	$1$	$1$		$0$	$20480$	$1.707476$	$-147281603041/215233605$	$1.05949$	$5.25106$	$[1, 0, 0, -31796, -4099995]$	\(y^2+xy=x^3-31796x-4099995\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$	$[]$
4335.c4	4335d4	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3 \cdot 5 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$8160$	$768$	$13$	$1$	$1$		$0$	$5120$	$1.014330$	$56667352321/15$	$1.03019$	$4.98655$	$[1, 0, 0, -23126, 1351701]$	\(y^2+xy=x^3-23126x+1351701\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$	$[]$
4335.c5	4335d3	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 17^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$4080$	$768$	$13$	$1$	$1$		$2$	$5120$	$1.014330$	$111284641/50625$	$1.02534$	$4.24228$	$[1, 0, 0, -2896, -27985]$	\(y^2+xy=x^3-2896x-27985\)	2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$	$[]$
4335.c6	4335d2	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 17^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$4080$	$768$	$13$	$1$	$1$		$2$	$2560$	$0.667755$	$13997521/225$	$0.96230$	$3.99472$	$[1, 0, 0, -1451, 20856]$	\(y^2+xy=x^3-1451x+20856\)	2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$	$[]$
4335.c7	4335d1	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( - 3 \cdot 5 \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$8160$	$768$	$13$	$1$	$1$		$1$	$1280$	$0.321182$	$-1/15$	$1.19808$	$3.24344$	$[1, 0, 0, -6, 915]$	\(y^2+xy=x^3-6x+915\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$	$[]$
4335.c8	4335d6	4335.c	4335d	$8$	$16$	\( 3 \cdot 5 \cdot 17^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 17^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$8160$	$768$	$13$	$1$	$1$		$0$	$10240$	$1.360903$	$4733169839/3515625$	$1.05585$	$4.69010$	$[1, 0, 0, 10109, -207454]$	\(y^2+xy=x^3+10109x-207454\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 68.24.0-4.d.1.1, $\ldots$	$[]$
4335.d1	4335a1	4335.d	4335a	$1$	$1$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5 \cdot 17^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$1$	$1$		$0$	$9792$	$1.202499$	$35651584/405$	$1.03043$	$4.78299$	$[0, -1, 1, -13101, 575867]$	\(y^2+y=x^3-x^2-13101x+575867\)	10.2.0.a.1	$[]$
4335.e1	4335c2	4335.e	4335c	$2$	$3$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{9} \cdot 17^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$510$	$16$	$0$	$1$	$1$		$0$	$352512$	$3.100842$	$17968412610002944/158203125$	$1.13557$	$7.85237$	$[0, -1, 1, -68932665, -220260749857]$	\(y^2+y=x^3-x^2-68932665x-220260749857\)	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 51.8.0-3.a.1.1, 510.16.0.?	$[]$
4335.e2	4335c1	4335.e	4335c	$2$	$3$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{12} \cdot 5^{3} \cdot 17^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$510$	$16$	$0$	$1$	$1$		$0$	$117504$	$2.551533$	$115220905984/66430125$	$1.23689$	$6.42455$	$[0, -1, 1, -1280655, 34490306]$	\(y^2+y=x^3-x^2-1280655x+34490306\)	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 51.8.0-3.a.1.2, 510.16.0.?	$[]$
4335.f1	4335e2	4335.f	4335e	$2$	$3$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5^{9} \cdot 17^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$4.052307060$	$1$		$0$	$20736$	$1.684235$	$17968412610002944/158203125$	$1.13557$	$5.82248$	$[0, 1, 1, -238521, -44916415]$	\(y^2+y=x^3+x^2-238521x-44916415\)	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[(-1131/2, 101/2)]$
4335.f2	4335e1	4335.f	4335e	$2$	$3$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{12} \cdot 5^{3} \cdot 17^{4} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1.350769020$	$1$		$8$	$6912$	$1.134928$	$115220905984/66430125$	$1.23689$	$4.39466$	$[0, 1, 1, -4431, 5456]$	\(y^2+y=x^3+x^2-4431x+5456\)	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[(-6, 178)]$
4335.g1	4335f1	4335.g	4335f	$1$	$1$	\( 3 \cdot 5 \cdot 17^{2} \)	\( 3^{4} \cdot 5 \cdot 17^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$10$	$2$	$0$	$0.270223130$	$1$		$4$	$576$	$-0.214107$	$35651584/405$	$1.03043$	$2.75310$	$[0, 1, 1, -45, 101]$	\(y^2+y=x^3+x^2-45x+101\)	10.2.0.a.1	$[(3, 1)]$