Elliptic curves over $\Q$ of conductor 1815

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
1815.a1	1815c1	1815.a	1815c	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3 \cdot 5^{2} \cdot 11^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$2112$	$0.858575$	$205379/75$	$0.85570$	$4.50618$	$[1, 0, 0, -1636, 15335]$	\(y^2+xy=x^3-1636x+15335\)	2.3.0.a.1, 12.6.0.f.1, 44.6.0.c.1, 66.6.0.a.1, 132.12.0.?	$[]$
1815.a2	1815c2	1815.a	1815c	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{2} \cdot 5^{4} \cdot 11^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$0$	$4224$	$1.205149$	$5929741/5625$	$0.92615$	$4.95434$	$[1, 0, 0, 5019, 109836]$	\(y^2+xy=x^3+5019x+109836\)	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$
1815.b1	1815e2	1815.b	1815e	$2$	$3$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{6} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$6$	$16$	$0$	$5.615713554$	$1$		$0$	$14256$	$1.925472$	$-196566176333824/421875$	$1.06963$	$6.94247$	$[0, 1, 1, -724951, -237822920]$	\(y^2+y=x^3+x^2-724951x-237822920\)	3.8.0-3.a.1.1, 6.16.0-6.b.1.1	$[(4421/2, 141371/2)]$
1815.b2	1815e1	1815.b	1815e	$2$	$3$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{8} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$6$	$16$	$0$	$1.871904518$	$1$		$8$	$4752$	$1.376167$	$-123633664/492075$	$1.03272$	$5.31461$	$[0, 1, 1, -6211, -530909]$	\(y^2+y=x^3+x^2-6211x-530909\)	3.8.0-3.a.1.2, 6.16.0-6.b.1.2	$[(107, 202)]$
1815.c1	1815d2	1815.c	1815d	$2$	$3$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{6} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$66$	$16$	$0$	$0.273856949$	$1$		$4$	$1296$	$0.726525$	$-196566176333824/421875$	$1.06963$	$5.02514$	$[0, 1, 1, -5991, 176501]$	\(y^2+y=x^3+x^2-5991x+176501\)	3.4.0.a.1, 6.8.0.b.1, 33.8.0-3.a.1.1, 66.16.0-6.b.1.1	$[(27, 187)]$
1815.c2	1815d1	1815.c	1815d	$2$	$3$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$66$	$16$	$0$	$0.091285649$	$1$		$8$	$432$	$0.177219$	$-123633664/492075$	$1.03272$	$3.39728$	$[0, 1, 1, -51, 380]$	\(y^2+y=x^3+x^2-51x+380\)	3.4.0.a.1, 6.8.0.b.1, 33.8.0-3.a.1.2, 66.16.0-6.b.1.2	$[(-6, 22)]$
1815.d1	1815a7	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3^{4} \cdot 5 \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.121	2B	$5280$	$768$	$13$	$1.666073956$	$1$		$2$	$5120$	$1.489817$	$1114544804970241/405$	$1.07354$	$6.53460$	$[1, 1, 0, -261362, 51320691]$	\(y^2+xy=x^3+x^2-261362x+51320691\)	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, $\ldots$	$[(270, 591)]$
1815.d2	1815a5	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3^{8} \cdot 5^{2} \cdot 11^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.123	2Cs	$2640$	$768$	$13$	$3.332147913$	$1$		$2$	$2560$	$1.143244$	$272223782641/164025$	$1.03897$	$5.42619$	$[1, 1, 0, -16337, 796536]$	\(y^2+xy=x^3+x^2-16337x+796536\)	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, $\ldots$	$[(783/2, 17367/2)]$
1815.d3	1815a8	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{16} \cdot 5 \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.134	2B	$5280$	$768$	$13$	$6.664295827$	$1$		$0$	$5120$	$1.489817$	$-147281603041/215233605$	$1.05949$	$5.51224$	$[1, 1, 0, -13312, 1104481]$	\(y^2+xy=x^3+x^2-13312x+1104481\)	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, $\ldots$	$[(6871/6, 488797/6)]$
1815.d4	1815a3	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3 \cdot 5 \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$5280$	$768$	$13$	$6.664295827$	$1$		$0$	$1280$	$0.796670$	$56667352321/15$	$1.03019$	$5.21704$	$[1, 1, 0, -9682, -370751]$	\(y^2+xy=x^3+x^2-9682x-370751\)	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, $\ldots$	$[(555/2, 7369/2)]$
1815.d5	1815a4	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3^{4} \cdot 5^{4} \cdot 11^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.44	2Cs	$2640$	$768$	$13$	$1.666073956$	$1$		$6$	$1280$	$0.796670$	$111284641/50625$	$1.02534$	$4.38642$	$[1, 1, 0, -1212, 7011]$	\(y^2+xy=x^3+x^2-1212x+7011\)	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, $\ldots$	$[(42, 159)]$
1815.d6	1815a2	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3^{2} \cdot 5^{2} \cdot 11^{6} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.48.0.3	2Cs	$2640$	$768$	$13$	$3.332147913$	$1$		$4$	$640$	$0.450097$	$13997521/225$	$0.96230$	$4.11013$	$[1, 1, 0, -607, -5936]$	\(y^2+xy=x^3+x^2-607x-5936\)	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, $\ldots$	$[(48, 256)]$
1815.d7	1815a1	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3 \cdot 5 \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.48.0.1	2B	$5280$	$768$	$13$	$6.664295827$	$1$		$1$	$320$	$0.103523$	$-1/15$	$1.19808$	$3.27168$	$[1, 1, 0, -2, -249]$	\(y^2+xy=x^3+x^2-2x-249\)	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, $\ldots$	$[(550/7, 10443/7)]$
1815.d8	1815a6	1815.d	1815a	$8$	$16$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{2} \cdot 5^{8} \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.48.0.197	2B	$5280$	$768$	$13$	$0.833036978$	$1$		$6$	$2560$	$1.143244$	$4733169839/3515625$	$1.05585$	$4.88620$	$[1, 1, 0, 4233, 58194]$	\(y^2+xy=x^3+x^2+4233x+58194\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 44.24.0-4.d.1.1, $\ldots$	$[(18, 366)]$
1815.e1	1815b1	1815.e	1815b	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \)	\( 3 \cdot 5^{2} \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$1$	$192$	$-0.340373$	$205379/75$	$0.85570$	$2.58885$	$[1, 0, 1, -14, -13]$	\(y^2+xy+y=x^3-14x-13\)	2.3.0.a.1, 12.6.0.f.1, 44.6.0.c.1, 66.6.0.a.1, 132.12.0.?	$[]$
1815.e2	1815b2	1815.e	1815b	$2$	$2$	\( 3 \cdot 5 \cdot 11^{2} \)	\( - 3^{2} \cdot 5^{4} \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$132$	$12$	$0$	$1$	$1$		$0$	$384$	$0.006201$	$5929741/5625$	$0.92615$	$3.03700$	$[1, 0, 1, 41, -79]$	\(y^2+xy+y=x^3+41x-79\)	2.3.0.a.1, 12.6.0.f.1, 22.6.0.a.1, 132.12.0.?	$[]$