Elliptic curves over $\Q$ of conductor 225

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
225.a1	225e1	225.a	225e	$2$	$5$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{7} \cdot 5^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$30$	$48$	$1$	$0.025588090$	$1$		$18$	$48$	$-0.043792$	$-102400/3$	$1.04391$	$4.54487$	$[0, 0, 1, -75, 256]$	\(y^2+y=x^3-75x+256\)	5.12.0.a.2, 6.2.0.a.1, 10.24.0-5.a.2.1, 15.24.0-5.a.2.2, 30.48.1-30.d.2.1	$[(-5, 22)]$
225.a2	225e2	225.a	225e	$2$	$5$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{11} \cdot 5^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$30$	$48$	$1$	$0.127940452$	$1$		$10$	$240$	$0.760927$	$20480/243$	$1.13104$	$5.97569$	$[0, 0, 1, 375, -12344]$	\(y^2+y=x^3+375x-12344\)	5.12.0.a.1, 6.2.0.a.1, 10.24.0-5.a.1.2, 15.24.0-5.a.1.2, 30.48.1-30.d.1.1	$[(100, 1012)]$
225.b1	225c7	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( 3^{10} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.49	2B	$480$	$768$	$13$	$1$	$1$		$0$	$768$	$1.644896$	$1114544804970241/405$	$1.07354$	$9.39708$	$[1, -1, 1, -486005, 130530872]$	\(y^2+xy+y=x^3-x^2-486005x+130530872\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 12.12.0-4.c.1.1, $\ldots$	$[]$
225.b2	225c5	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( 3^{14} \cdot 5^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.53	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$384$	$1.298321$	$272223782641/164025$	$1.03897$	$7.86141$	$[1, -1, 1, -30380, 2044622]$	\(y^2+xy+y=x^3-x^2-30380x+2044622\)	2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 12.24.0-4.b.1.2, 16.96.0-8.k.1.3, $\ldots$	$[]$
225.b3	225c8	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{22} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.65	2B	$480$	$768$	$13$	$1$	$1$		$0$	$768$	$1.644896$	$-147281603041/215233605$	$1.05949$	$7.98063$	$[1, -1, 1, -24755, 2820872]$	\(y^2+xy+y=x^3-x^2-24755x+2820872\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 12.12.0-4.c.1.2, 16.48.0.u.2, $\ldots$	$[]$
225.b4	225c3	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( 3^{7} \cdot 5^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.15	2B	$480$	$768$	$13$	$1$	$1$		$0$	$192$	$0.951748$	$56667352321/15$	$1.03019$	$7.57164$	$[1, -1, 1, -18005, -925378]$	\(y^2+xy+y=x^3-x^2-18005x-925378\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 16.48.0-16.g.1.11, 24.48.0-24.by.2.6, $\ldots$	$[]$
225.b5	225c4	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( 3^{10} \cdot 5^{10} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.96.0.61	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$192$	$0.951748$	$111284641/50625$	$1.02534$	$6.42084$	$[1, -1, 1, -2255, 19622]$	\(y^2+xy+y=x^3-x^2-2255x+19622\)	2.6.0.a.1, 4.24.0.b.1, 8.96.0-8.b.2.7, 24.192.1-24.n.1.16, 40.192.1-40.s.1.9, $\ldots$	$[]$
225.b6	225c2	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( 3^{8} \cdot 5^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.2	2Cs	$240$	$768$	$13$	$1$	$1$		$2$	$96$	$0.605174$	$13997521/225$	$0.96230$	$6.03805$	$[1, -1, 1, -1130, -14128]$	\(y^2+xy+y=x^3-x^2-1130x-14128\)	2.6.0.a.1, 4.24.0-4.b.1.2, 8.48.0-8.i.1.7, 16.96.0-16.d.2.10, 24.96.0-24.bb.2.16, $\ldots$	$[]$
225.b7	225c1	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{7} \cdot 5^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.7	2B	$480$	$768$	$13$	$1$	$1$		$3$	$48$	$0.258600$	$-1/15$	$1.19808$	$4.87641$	$[1, -1, 1, -5, -628]$	\(y^2+xy+y=x^3-x^2-5x-628\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 16.48.0-16.g.1.15, 24.48.0-24.bz.1.14, $\ldots$	$[]$
225.b8	225c6	225.b	225c	$8$	$16$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{8} \cdot 5^{14} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.195	2B	$480$	$768$	$13$	$1$	$1$		$0$	$384$	$1.298321$	$4733169839/3515625$	$1.05585$	$7.11327$	$[1, -1, 1, 7870, 141122]$	\(y^2+xy+y=x^3-x^2+7870x+141122\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 16.96.0-8.n.2.4, 24.96.1.cv.2, $\ldots$	$[]$
225.c1	225a2	225.c	225a	$2$	$3$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{9} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$5$	5.30.0.2	5Ns.2.1				$0.460920105$	$1$		$4$	$24$	$-0.228919$	$0$		$3.79629$	$[0, 0, 1, 0, -34]$	\(y^2+y=x^3-34\)		$[(6, 13)]$
225.c2	225a1	225.c	225a	$2$	$3$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{2} \)	$1$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$5$	5.30.0.2	5Ns.2.1				$0.153640035$	$1$		$6$	$8$	$-0.778225$	$0$		$2.57924$	$[0, 0, 1, 0, 1]$	\(y^2+y=x^3+1\)		$[(1, 1)]$
225.d1	225b2	225.d	225b	$2$	$3$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{9} \cdot 5^{8} \)	$0$	$\mathsf{trivial}$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3, 5$	5.30.0.2, 27.648.18.4	5Ns.2.1, 3B.1.2				$1$	$1$		$0$	$120$	$0.575800$	$0$		$5.57924$	$[0, 0, 1, 0, -4219]$	\(y^2+y=x^3-4219\)		$[]$
225.d2	225b1	225.d	225b	$2$	$3$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{8} \)	$0$	$\Z/3\Z$	$\Q(\sqrt{-3})$	$-3$	$N(\mathrm{U}(1))$		✓	$3, 5$	5.30.0.2, 27.648.18.1	5Ns.2.1, 3B.1.1				$1$	$1$		$2$	$40$	$0.026494$	$0$		$4.36219$	$[0, 0, 1, 0, 156]$	\(y^2+y=x^3+156\)		$[]$
225.e1	225d2	225.e	225d	$2$	$5$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{7} \cdot 5^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.2	5B.4.2	$30$	$48$	$1$	$1$	$1$		$0$	$240$	$0.760927$	$-102400/3$	$1.04391$	$6.32781$	$[0, 0, 1, -1875, 32031]$	\(y^2+y=x^3-1875x+32031\)	5.12.0.a.2, 6.2.0.a.1, 10.24.0-5.a.2.2, 15.24.0-5.a.2.1, 30.48.1-30.d.2.2	$[]$
225.e2	225d1	225.e	225d	$2$	$5$	\( 3^{2} \cdot 5^{2} \)	\( - 3^{11} \cdot 5^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.12.0.1	5B.4.1	$30$	$48$	$1$	$1$	$1$		$0$	$48$	$-0.043792$	$20480/243$	$1.13104$	$4.19275$	$[0, 0, 1, 15, -99]$	\(y^2+y=x^3+15x-99\)	5.12.0.a.1, 6.2.0.a.1, 10.24.0-5.a.1.1, 15.24.0-5.a.1.1, 30.48.1-30.d.1.2	$[]$