Elliptic curves over $\Q$ of conductor 3315

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
3315.a1	3315b3	3315.a	3315b	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3 \cdot 5 \cdot 13 \cdot 17^{4} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$26520$	$48$	$0$	$5.425373837$	$1$		$6$	$1792$	$0.404955$	$126574061279329/16286595$	$0.90554$	$4.00580$	$[1, 1, 1, -1046, -13456]$	\(y^2+xy+y=x^3+x^2-1046x-13456\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 136.12.0.?, 260.12.0.?, $\ldots$	$[(-19, 8), (37, -4)]$
3315.a2	3315b2	3315.a	3315b	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	2.6.0.1	2Cs	$13260$	$48$	$0$	$1.356343459$	$1$		$26$	$896$	$0.058381$	$39616946929/10989225$	$0.84706$	$3.01035$	$[1, 1, 1, -71, -196]$	\(y^2+xy+y=x^3+x^2-71x-196\)	2.6.0.a.1, 12.12.0-2.a.1.1, 68.12.0-2.a.1.1, 204.24.0.?, 260.12.0.?, $\ldots$	$[(-4, 8), (22, 86)]$
3315.a3	3315b1	3315.a	3315b	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5 \cdot 13 \cdot 17 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$26520$	$48$	$0$	$1.356343459$	$1$		$13$	$448$	$-0.288192$	$1948441249/89505$	$0.80465$	$2.63875$	$[1, 1, 1, -26, 38]$	\(y^2+xy+y=x^3+x^2-26x+38\)	2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 68.12.0-4.c.1.2, 260.12.0.?, $\ldots$	$[(-6, 7), (4, 2)]$
3315.a4	3315b4	3315.a	3315b	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3 \cdot 5^{4} \cdot 13^{4} \cdot 17 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.1	2B	$26520$	$48$	$0$	$1.356343459$	$1$		$14$	$1792$	$0.404955$	$688699320191/910381875$	$0.88763$	$3.39347$	$[1, 1, 1, 184, -1012]$	\(y^2+xy+y=x^3+x^2+184x-1012\)	2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 68.12.0-4.c.1.1, 102.6.0.?, $\ldots$	$[(8, 28), (11, 44)]$
3315.b1	3315e3	3315.b	3315e	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 13 \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$1768$	$48$	$0$	$1$	$1$		$0$	$4096$	$0.934161$	$420339554066191969/244298925$	$0.95222$	$5.00602$	$[1, 0, 0, -15606, -751689]$	\(y^2+xy=x^3-15606x-751689\)	2.3.0.a.1, 4.12.0-4.c.1.2, 26.6.0.b.1, 52.24.0-52.g.1.1, 136.24.0.?, $\ldots$	$[]$
3315.b2	3315e2	3315.b	3315e	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5^{4} \cdot 13^{2} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$884$	$48$	$0$	$1$	$1$		$2$	$2048$	$0.587588$	$104413920565969/2472575625$	$1.15696$	$3.98205$	$[1, 0, 0, -981, -11664]$	\(y^2+xy=x^3-981x-11664\)	2.6.0.a.1, 4.12.0-2.a.1.1, 52.24.0-52.b.1.2, 68.24.0-68.b.1.1, 884.48.0.?	$[]$
3315.b3	3315e1	3315.b	3315e	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{2} \cdot 5^{2} \cdot 13^{4} \cdot 17 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$1768$	$48$	$0$	$1$	$1$		$3$	$1024$	$0.241014$	$278317173889/109245825$	$0.94810$	$3.25084$	$[1, 0, 0, -136, 335]$	\(y^2+xy=x^3-136x+335\)	2.3.0.a.1, 4.12.0-4.c.1.1, 34.6.0.a.1, 68.24.0-68.g.1.2, 104.24.0.?, $\ldots$	$[]$
3315.b4	3315e4	3315.b	3315e	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3^{8} \cdot 5^{8} \cdot 13 \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$1768$	$48$	$0$	$1$	$1$		$0$	$4096$	$0.934161$	$210751100351/566398828125$	$0.99333$	$4.25810$	$[1, 0, 0, 124, -36195]$	\(y^2+xy=x^3+124x-36195\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 52.12.0-4.c.1.2, 68.12.0-4.c.1.1, $\ldots$	$[]$
3315.c1	3315f1	3315.c	3315f	$2$	$2$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{4} \cdot 5 \cdot 13 \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.3	2B	$26520$	$48$	$0$	$1.164824499$	$1$		$5$	$320$	$-0.313741$	$887503681/89505$	$0.91820$	$2.54174$	$[1, 0, 0, -20, -33]$	\(y^2+xy=x^3-20x-33\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.4, 2210.6.0.?, 4420.24.0.?, $\ldots$	$[(-3, 3)]$
3315.c2	3315f2	3315.c	3315f	$2$	$2$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3^{2} \cdot 5^{2} \cdot 13^{2} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.6.0.5	2B	$26520$	$48$	$0$	$0.582412249$	$1$		$8$	$640$	$0.032832$	$1723683599/10989225$	$0.85519$	$2.90789$	$[1, 0, 0, 25, -150]$	\(y^2+xy=x^3+25x-150\)	2.3.0.a.1, 4.6.0.a.1, 24.12.0-4.a.1.1, 4420.12.0.?, 8840.24.0.?, $\ldots$	$[(7, 16)]$
3315.d1	3315a1	3315.d	3315a	$1$	$1$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3^{5} \cdot 5^{5} \cdot 13^{3} \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6630$	$2$	$0$	$1$	$1$		$0$	$1800$	$0.702256$	$-30558612127744/28361896875$	$0.94057$	$3.94853$	$[0, -1, 1, -651, 10541]$	\(y^2+y=x^3-x^2-651x+10541\)	6630.2.0.?	$[]$
3315.e1	3315d1	3315.e	3315d	$1$	$1$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3 \cdot 5 \cdot 13 \cdot 17 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓					$6630$	$2$	$0$	$1$	$1$		$0$	$168$	$-0.601440$	$-16777216/3315$	$0.84101$	$2.08843$	$[0, -1, 1, -5, -4]$	\(y^2+y=x^3-x^2-5x-4\)	6630.2.0.?	$[]$
3315.f1	3315c4	3315.f	3315c	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{3} \cdot 5^{4} \cdot 13^{12} \cdot 17^{2} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$312$	$48$	$0$	$6.749071061$	$1$		$4$	$239616$	$2.911583$	$1968666709544018637994033129/113621848881699526875$	$1.02739$	$7.75296$	$[1, 1, 0, -26110558, 51340332637]$	\(y^2+xy=x^3+x^2-26110558x+51340332637\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 104.24.0.?, 312.48.0.?	$[(185516, 79782167)]$
3315.f2	3315c3	3315.f	3315c	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{12} \cdot 5^{4} \cdot 13^{3} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$312$	$48$	$0$	$1.687267765$	$1$		$0$	$239616$	$2.911583$	$70141892778055497175333129/5090453819946781723125$	$1.02034$	$7.34160$	$[1, 1, 0, -8591808, -9068791113]$	\(y^2+xy=x^3+x^2-8591808x-9068791113\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[(41439/2, 8014011/2)]$
3315.f3	3315c2	3315.f	3315c	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( 3^{6} \cdot 5^{8} \cdot 13^{6} \cdot 17^{4} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$3.374535530$	$1$		$4$	$119808$	$2.565010$	$568832774079017834683129/114800389711906640625$	$1.00981$	$6.74765$	$[1, 1, 0, -1726183, 703739512]$	\(y^2+xy=x^3+x^2-1726183x+703739512\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 52.24.0-52.b.1.2, 156.48.0.?	$[(1848, 60956)]$
3315.f4	3315c1	3315.f	3315c	$4$	$4$	\( 3 \cdot 5 \cdot 13 \cdot 17 \)	\( - 3^{3} \cdot 5^{16} \cdot 13^{3} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$312$	$48$	$0$	$6.749071061$	$1$		$1$	$59904$	$2.218437$	$1292603583867446566871/2615843353271484375$	$1.00195$	$6.10964$	$[1, 1, 0, 226942, 65848887]$	\(y^2+xy=x^3+x^2+226942x+65848887\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[(6694/5, 1493137/5)]$