Elliptic curves over $\Q$ of conductor 25215

Results (19 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
25215.a1	25215d1	25215.a	25215d	$1$	$1$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{3} \cdot 5^{4} \cdot 41^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.603898174$	$1$		$6$	$330624$	$2.035175$	$-223522816/16875$	$0.88787$	$4.84019$	$[0, -1, 1, -252710, 52073006]$	\(y^2+y=x^3-x^2-252710x+52073006\)	6.2.0.a.1	$[(-560, 4202)]$
25215.b1	25215i1	25215.b	25215i	$1$	$1$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{3} \cdot 5^{4} \cdot 41^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$6$	$2$	$0$	$0.138615308$	$1$		$8$	$8064$	$0.178390$	$-223522816/16875$	$0.88787$	$2.64176$	$[0, 1, 1, -150, 704]$	\(y^2+y=x^3+x^2-150x+704\)	6.2.0.a.1	$[(6, 7)]$
25215.c1	25215b1	25215.c	25215b	$1$	$1$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{9} \cdot 5^{4} \cdot 41^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12$	$2$	$0$	$1$	$4$	$2$	$0$	$743904$	$2.526096$	$21708480289/12301875$	$1.00114$	$5.27958$	$[1, 1, 1, -1161606, 68959728]$	\(y^2+xy+y=x^3+x^2-1161606x+68959728\)	12.2.0.a.1	$[]$
25215.d1	25215f1	25215.d	25215f	$1$	$1$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{9} \cdot 5^{4} \cdot 41^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$12$	$2$	$0$	$0.290951680$	$1$		$20$	$18144$	$0.669310$	$21708480289/12301875$	$1.00114$	$3.08116$	$[1, 0, 0, -691, 950]$	\(y^2+xy=x^3-691x+950\)	12.2.0.a.1	$[(53, 311), (-1, 41)]$
25215.e1	25215e1	25215.e	25215e	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 41^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$820$	$12$	$0$	$1$	$1$		$1$	$53760$	$1.316833$	$24137569/9225$	$0.94928$	$3.87567$	$[1, 0, 0, -10121, -229224]$	\(y^2+xy=x^3-10121x-229224\)	2.3.0.a.1, 20.6.0.b.1, 82.6.0.?, 820.12.0.?	$[]$
25215.e2	25215e2	25215.e	25215e	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{4} \cdot 5 \cdot 41^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$820$	$12$	$0$	$1$	$1$		$0$	$107520$	$1.663406$	$756058031/680805$	$0.87543$	$4.21551$	$[1, 0, 0, 31904, -1632859]$	\(y^2+xy=x^3+31904x-1632859\)	2.3.0.a.1, 20.6.0.a.1, 164.6.0.?, 820.12.0.?	$[]$
25215.f1	25215h8	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{4} \cdot 5 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$19680$	$768$	$13$	$10.82426373$	$1$		$0$	$266240$	$2.147655$	$1114544804970241/405$	$1.07354$	$5.61693$	$[1, 0, 0, -3630995, -2663397180]$	\(y^2+xy=x^3-3630995x-2663397180\)	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, $\ldots$	$[(1425481/24, 801818593/24)]$
25215.f2	25215h6	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 41^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$9840$	$768$	$13$	$5.412131868$	$1$		$2$	$133120$	$1.801083$	$272223782641/164025$	$1.03897$	$4.79629$	$[1, 0, 0, -226970, -41617125]$	\(y^2+xy=x^3-226970x-41617125\)	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, $\ldots$	$[(18070/3, 2326295/3)]$
25215.f3	25215h7	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{16} \cdot 5 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$19680$	$768$	$13$	$2.706065934$	$1$		$0$	$266240$	$2.147655$	$-147281603041/215233605$	$1.05949$	$4.86000$	$[1, 0, 0, -184945, -57494170]$	\(y^2+xy=x^3-184945x-57494170\)	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, $\ldots$	$[(15443/2, 1890811/2)]$
25215.f4	25215h4	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3 \cdot 5 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$19680$	$768$	$13$	$10.82426373$	$1$		$0$	$66560$	$1.454508$	$56667352321/15$	$1.03019$	$4.64144$	$[1, 0, 0, -134515, 18977882]$	\(y^2+xy=x^3-134515x+18977882\)	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, $\ldots$	$[(65422/11, 13238498/11)]$
25215.f5	25215h3	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 41^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$9840$	$768$	$13$	$2.706065934$	$1$		$6$	$66560$	$1.454508$	$111284641/50625$	$1.02534$	$4.02647$	$[1, 0, 0, -16845, -390600]$	\(y^2+xy=x^3-16845x-390600\)	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, $\ldots$	$[(-105, 525)]$
25215.f6	25215h2	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 41^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$9840$	$768$	$13$	$5.412131868$	$1$		$4$	$33280$	$1.107935$	$13997521/225$	$0.96230$	$3.82191$	$[1, 0, 0, -8440, 293567]$	\(y^2+xy=x^3-8440x+293567\)	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, $\ldots$	$[(499, 10723)]$
25215.f7	25215h1	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3 \cdot 5 \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$19680$	$768$	$13$	$10.82426373$	$1$		$1$	$16640$	$0.761361$	$-1/15$	$1.19808$	$3.20115$	$[1, 0, 0, -35, 12840]$	\(y^2+xy=x^3-35x+12840\)	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, $\ldots$	$[(44697/19, 9055734/19)]$
25215.f8	25215h5	25215.f	25215h	$8$	$16$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 41^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$19680$	$768$	$13$	$1.353032967$	$1$		$2$	$133120$	$1.801083$	$4733169839/3515625$	$1.05585$	$4.39649$	$[1, 0, 0, 58800, -2917143]$	\(y^2+xy=x^3+58800x-2917143\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[(509, 12353)]$
25215.g1	25215a1	25215.g	25215a	$1$	$1$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{7} \cdot 5^{4} \cdot 41^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$246$	$2$	$0$	$5.535474616$	$1$		$0$	$188160$	$2.030350$	$53838872576/56041875$	$1.29887$	$4.63639$	$[0, -1, 1, 132239, -16585758]$	\(y^2+y=x^3-x^2+132239x-16585758\)	246.2.0.?	$[(16536/11, 2667922/11)]$
25215.h1	25215c1	25215.h	25215c	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{8} \cdot 5^{4} \cdot 41^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1640$	$48$	$1$	$1$	$1$		$1$	$40960$	$0.993761$	$233858751281/4100625$	$0.96749$	$3.68209$	$[1, 1, 0, -5262, -146889]$	\(y^2+xy=x^3+x^2-5262x-146889\)	2.3.0.a.1, 4.12.0.f.1, 40.24.0.eb.1, 82.6.0.?, 164.24.0.?, $\ldots$	$[]$
25215.h2	25215c2	25215.h	25215c	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{16} \cdot 5^{2} \cdot 41^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1640$	$48$	$1$	$1$	$4$	$2$	$0$	$81920$	$1.340334$	$-4173281/1076168025$	$1.15476$	$3.88667$	$[1, 1, 0, -137, -414414]$	\(y^2+xy=x^3+x^2-137x-414414\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 40.24.0.dk.1, 164.12.0.?, $\ldots$	$[]$
25215.i1	25215g1	25215.i	25215g	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( 3^{8} \cdot 5^{4} \cdot 41^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1640$	$48$	$1$	$5.019365493$	$1$		$3$	$1679360$	$2.850548$	$233858751281/4100625$	$0.96749$	$5.88051$	$[1, 0, 1, -8846298, -9973354697]$	\(y^2+xy+y=x^3-8846298x-9973354697\)	2.3.0.a.1, 4.12.0.f.1, 40.24.0.eb.1, 82.6.0.?, 164.24.0.?, $\ldots$	$[(-1621, 11190)]$
25215.i2	25215g2	25215.i	25215g	$2$	$2$	\( 3 \cdot 5 \cdot 41^{2} \)	\( - 3^{16} \cdot 5^{2} \cdot 41^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1640$	$48$	$1$	$10.03873098$	$1$		$0$	$3358720$	$3.197121$	$-4173281/1076168025$	$1.15476$	$6.08509$	$[1, 0, 1, -231173, -28557902347]$	\(y^2+xy+y=x^3-231173x-28557902347\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 40.24.0.dk.1, 164.12.0.?, $\ldots$	$[(318669/4, 178876945/4)]$