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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
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	$0.025588090$	$1$		$18$	$48$	$-0.043792$	$-102400/3$	$[0, 0, 1, -75, 256]$	\(y^2+y=x^3-75x+256\)
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	$0.127940452$	$1$		$10$	$240$	$0.760927$	$20480/243$	$[0, 0, 1, 375, -12344]$	\(y^2+y=x^3+375x-12344\)
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	$1$	$1$		$0$	$768$	$1.644896$	$1114544804970241/405$	$[1, -1, 1, -486005, 130530872]$	\(y^2+xy+y=x^3-x^2-486005x+130530872\)
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	$1$	$1$		$2$	$384$	$1.298321$	$272223782641/164025$	$[1, -1, 1, -30380, 2044622]$	\(y^2+xy+y=x^3-x^2-30380x+2044622\)
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	$1$	$1$		$0$	$768$	$1.644896$	$-147281603041/215233605$	$[1, -1, 1, -24755, 2820872]$	\(y^2+xy+y=x^3-x^2-24755x+2820872\)
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	$1$	$1$		$0$	$192$	$0.951748$	$56667352321/15$	$[1, -1, 1, -18005, -925378]$	\(y^2+xy+y=x^3-x^2-18005x-925378\)
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	$1$	$1$		$2$	$192$	$0.951748$	$111284641/50625$	$[1, -1, 1, -2255, 19622]$	\(y^2+xy+y=x^3-x^2-2255x+19622\)
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	$1$	$1$		$2$	$96$	$0.605174$	$13997521/225$	$[1, -1, 1, -1130, -14128]$	\(y^2+xy+y=x^3-x^2-1130x-14128\)
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	$1$	$1$		$3$	$48$	$0.258600$	$-1/15$	$[1, -1, 1, -5, -628]$	\(y^2+xy+y=x^3-x^2-5x-628\)
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	$1$	$1$		$0$	$384$	$1.298321$	$4733169839/3515625$	$[1, -1, 1, 7870, 141122]$	\(y^2+xy+y=x^3-x^2+7870x+141122\)
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	$0.460920105$	$1$		$4$	$24$	$-0.228919$	$0$	$[0, 0, 1, 0, -34]$	\(y^2+y=x^3-34\)
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	$0.153640035$	$1$		$6$	$8$	$-0.778225$	$0$	$[0, 0, 1, 0, 1]$	\(y^2+y=x^3+1\)
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	$1$	$1$		$0$	$120$	$0.575800$	$0$	$[0, 0, 1, 0, -4219]$	\(y^2+y=x^3-4219\)
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	$1$	$1$		$2$	$40$	$0.026494$	$0$	$[0, 0, 1, 0, 156]$	\(y^2+y=x^3+156\)
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	$1$	$1$		$0$	$240$	$0.760927$	$-102400/3$	$[0, 0, 1, -1875, 32031]$	\(y^2+y=x^3-1875x+32031\)
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	$1$	$1$		$0$	$48$	$-0.043792$	$20480/243$	$[0, 0, 1, 15, -99]$	\(y^2+y=x^3+15x-99\)