Elliptic curves over $\Q$ of conductor 14415

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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
14415.a1	14415b2	14415.a	14415b	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 31^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1240$	$48$	$1$	$1$	$1$		$0$	$317440$	$2.516113$	$252316159759/164025$	$0.97252$	$5.96906$	$[1, 1, 1, -3921861, 2986102764]$	\(y^2+xy+y=x^3+x^2-3921861x+2986102764\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 40.24.0.dk.1, 124.12.0.?, $\ldots$	$[]$
14415.a2	14415b1	14415.a	14415b	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3^{4} \cdot 5^{4} \cdot 31^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1240$	$48$	$1$	$1$	$1$		$1$	$158720$	$2.169540$	$-32461759/50625$	$0.92162$	$5.17004$	$[1, 1, 1, -197986, 65095214]$	\(y^2+xy+y=x^3+x^2-197986x+65095214\)	2.3.0.a.1, 4.12.0.f.1, 40.24.0.eb.1, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[]$
14415.b1	14415c3	14415.b	14415c	$4$	$4$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 31^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.8	2B	$3720$	$48$	$0$	$2.442048902$	$1$		$4$	$122880$	$1.776777$	$543538277281/1569375$	$0.92064$	$4.97339$	$[1, 1, 1, -163390, -25425220]$	\(y^2+xy+y=x^3+x^2-163390x-25425220\)	2.3.0.a.1, 4.12.0-4.c.1.2, 120.24.0.?, 124.24.0.?, 3720.48.0.?	$[(-232, 363)]$
14415.b2	14415c2	14415.b	14415c	$4$	$4$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 31^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1860$	$48$	$0$	$4.884097804$	$1$		$4$	$61440$	$1.430204$	$374805361/216225$	$0.96767$	$4.21321$	$[1, 1, 1, -14435, -43288]$	\(y^2+xy+y=x^3+x^2-14435x-43288\)	2.6.0.a.1, 4.12.0-2.a.1.1, 60.24.0-60.b.1.6, 124.24.0.?, 1860.48.0.?	$[(242, 3151)]$
14415.b3	14415c1	14415.b	14415c	$4$	$4$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3 \cdot 5 \cdot 31^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.7	2B	$3720$	$48$	$0$	$9.768195608$	$1$		$3$	$30720$	$1.083630$	$111284641/465$	$0.83191$	$4.08641$	$[1, 1, 1, -9630, 358410]$	\(y^2+xy+y=x^3+x^2-9630x+358410\)	2.3.0.a.1, 4.12.0-4.c.1.1, 120.24.0.?, 248.24.0.?, 930.6.0.?, $\ldots$	$[(22980/17, 1381830/17)]$
14415.b4	14415c4	14415.b	14415c	$4$	$4$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3 \cdot 5 \cdot 31^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.6	2B	$3720$	$48$	$0$	$9.768195608$	$1$		$0$	$122880$	$1.776777$	$23862997439/13852815$	$1.00143$	$4.64697$	$[1, 1, 1, 57640, -273928]$	\(y^2+xy+y=x^3+x^2+57640x-273928\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 30.6.0.a.1, 60.12.0.g.1, $\ldots$	$[(8975/7, 1360444/7)]$
14415.c1	14415e2	14415.c	14415e	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 31^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.27	2B	$1240$	$48$	$1$	$0.765316265$	$1$		$6$	$10240$	$0.799121$	$252316159759/164025$	$0.97252$	$3.81744$	$[1, 0, 0, -4081, -100630]$	\(y^2+xy=x^3-4081x-100630\)	2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 40.24.0.dk.1, 124.12.0.?, $\ldots$	$[(-37, 26)]$
14415.c2	14415e1	14415.c	14415e	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3^{4} \cdot 5^{4} \cdot 31^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.11	2B	$1240$	$48$	$1$	$1.530632531$	$1$		$5$	$5120$	$0.452548$	$-32461759/50625$	$0.92162$	$3.01842$	$[1, 0, 0, -206, -2205]$	\(y^2+xy=x^3-206x-2205\)	2.3.0.a.1, 4.12.0.f.1, 40.24.0.eb.1, 62.6.0.b.1, 124.24.0.?, $\ldots$	$[(43, 241)]$
14415.d1	14415g7	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{4} \cdot 5 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$14880$	$768$	$13$	$1$	$1$		$0$	$122880$	$2.007862$	$1114544804970241/405$	$1.07354$	$5.76974$	$[1, 0, 0, -2075780, 1150945707]$	\(y^2+xy=x^3-2075780x+1150945707\)	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, $\ldots$	$[]$
14415.d2	14415g5	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 31^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$7440$	$768$	$13$	$1$	$1$		$2$	$61440$	$1.661289$	$272223782641/164025$	$1.03897$	$4.90118$	$[1, 0, 0, -129755, 17969952]$	\(y^2+xy=x^3-129755x+17969952\)	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, $\ldots$	$[]$
14415.d3	14415g8	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3^{16} \cdot 5 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$14880$	$768$	$13$	$1$	$1$		$0$	$122880$	$2.007862$	$-147281603041/215233605$	$1.05949$	$4.96861$	$[1, 0, 0, -105730, 24836297]$	\(y^2+xy=x^3-105730x+24836297\)	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, $\ldots$	$[]$
14415.d4	14415g3	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3 \cdot 5 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$14880$	$768$	$13$	$1$	$16$	$2$	$0$	$30720$	$1.314716$	$56667352321/15$	$1.03019$	$4.73729$	$[1, 0, 0, -76900, -8214415]$	\(y^2+xy=x^3-76900x-8214415\)	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, $\ldots$	$[]$
14415.d5	14415g4	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 31^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$7440$	$768$	$13$	$1$	$1$		$2$	$30720$	$1.314716$	$111284641/50625$	$1.02534$	$4.08641$	$[1, 0, 0, -9630, 167427]$	\(y^2+xy=x^3-9630x+167427\)	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, $\ldots$	$[]$
14415.d6	14415g2	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 31^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$7440$	$768$	$13$	$1$	$4$	$2$	$2$	$15360$	$0.968143$	$13997521/225$	$0.96230$	$3.86991$	$[1, 0, 0, -4825, -127600]$	\(y^2+xy=x^3-4825x-127600\)	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, $\ldots$	$[]$
14415.d7	14415g1	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3 \cdot 5 \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$14880$	$768$	$13$	$1$	$4$	$2$	$1$	$7680$	$0.621569$	$-1/15$	$1.19808$	$3.21289$	$[1, 0, 0, -20, -5553]$	\(y^2+xy=x^3-20x-5553\)	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, $\ldots$	$[]$
14415.d8	14415g6	14415.d	14415g	$8$	$16$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 31^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$14880$	$768$	$13$	$1$	$1$		$0$	$61440$	$1.661289$	$4733169839/3515625$	$1.05585$	$4.47804$	$[1, 0, 0, 33615, 1265850]$	\(y^2+xy=x^3+33615x+1265850\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$	$[]$
14415.e1	14415a2	14415.e	14415a	$2$	$3$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{2} \cdot 5^{3} \cdot 31^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$930$	$16$	$0$	$0.962068734$	$1$		$12$	$7920$	$0.500438$	$2612000948224/1125$	$1.01923$	$3.70291$	$[0, -1, 1, -2831, 58931]$	\(y^2+y=x^3-x^2-2831x+58931\)	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 93.8.0.?, 930.16.0.?	$[(31, 0), (29, 19)]$
14415.e2	14415a1	14415.e	14415a	$2$	$3$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{6} \cdot 5 \cdot 31^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$930$	$16$	$0$	$0.962068734$	$1$		$8$	$2640$	$-0.048868$	$8126464/3645$	$1.25017$	$2.37871$	$[0, -1, 1, -41, 62]$	\(y^2+y=x^3-x^2-41x+62\)	3.4.0.a.1, 10.2.0.a.1, 30.8.0.a.1, 93.8.0.?, 930.16.0.?	$[(8, 13), (5/2, 23/2)]$
14415.f1	14415d2	14415.f	14415d	$2$	$3$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{2} \cdot 5^{3} \cdot 31^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$30$	$16$	$0$	$1$	$1$		$0$	$245520$	$2.217430$	$2612000948224/1125$	$1.01923$	$5.85452$	$[0, 1, 1, -2720911, -1728412859]$	\(y^2+y=x^3+x^2-2720911x-1728412859\)	3.8.0-3.a.1.1, 10.2.0.a.1, 30.16.0-30.a.1.1	$[]$
14415.f2	14415d1	14415.f	14415d	$2$	$3$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{6} \cdot 5 \cdot 31^{8} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$30$	$16$	$0$	$1$	$1$		$2$	$81840$	$1.668125$	$8126464/3645$	$1.25017$	$4.53033$	$[0, 1, 1, -39721, -1458380]$	\(y^2+y=x^3+x^2-39721x-1458380\)	3.8.0-3.a.1.2, 10.2.0.a.1, 30.16.0-30.a.1.4	$[]$
14415.g1	14415f2	14415.g	14415f	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( 3^{6} \cdot 5^{2} \cdot 31^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1860$	$12$	$0$	$1$	$1$		$0$	$92160$	$1.731960$	$474734543401/564975$	$0.91952$	$4.95925$	$[1, 0, 1, -156183, -23745857]$	\(y^2+xy+y=x^3-156183x-23745857\)	2.3.0.a.1, 60.6.0.c.1, 124.6.0.?, 1860.12.0.?	$[]$
14415.g2	14415f1	14415.g	14415f	$2$	$2$	\( 3 \cdot 5 \cdot 31^{2} \)	\( - 3^{3} \cdot 5 \cdot 31^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1860$	$12$	$0$	$1$	$4$	$2$	$1$	$46080$	$1.385387$	$-47045881/129735$	$0.99639$	$4.17944$	$[1, 0, 1, -7228, -568459]$	\(y^2+xy+y=x^3-7228x-568459\)	2.3.0.a.1, 30.6.0.a.1, 124.6.0.?, 1860.12.0.?	$[]$

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