Elliptic curve search results

Results (24 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
4225.e2	4225n1	4225.e	4225n	$2$	$2$	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$5.572172126$	$1$		$3$	$24960$	$1.846424$	$4913$	$0.79101$	$5.51807$	$1$	$[1, 0, 0, -97263, -9408608]$	\(y^2+xy=x^3-97263x-9408608\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-177, 1595)]$	$1$
4225.h2	4225m1	4225.h	4225m	$2$	$2$	\( 5^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1.448847248$	$1$		$3$	$384$	$-0.240770$	$4913$	$0.79101$	$2.51807$	$1$	$[1, 1, 1, -23, -44]$	\(y^2+xy+y=x^3+x^2-23x-44\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-4, 3)]$	$1$
4225.k2	4225k1	4225.k	4225k	$2$	$2$	\( 5^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$2.946756332$	$1$		$3$	$1920$	$0.563949$	$4913$	$0.79101$	$3.67472$	$1$	$[1, 0, 1, -576, -4327]$	\(y^2+xy+y=x^3-576x-4327\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-9, 16)]$	$1$
4225.m2	4225j1	4225.m	4225j	$2$	$2$	\( 5^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$9.624222082$	$1$		$1$	$4992$	$1.041704$	$4913$	$0.79101$	$4.36142$	$1$	$[1, 1, 0, -3890, -76825]$	\(y^2+xy=x^3+x^2-3890x-76825\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-10046/17, 742763/17)]$	$1$
38025.t2	38025cv1	38025.t	38025cv	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 5^{3} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$119808$	$1.591011$	$4913$	$0.79101$	$4.07777$	$1$	$[1, -1, 1, -35015, 2039262]$	\(y^2+xy+y=x^3-x^2-35015x+2039262\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
38025.u2	38025cu1	38025.u	38025cu	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 5^{9} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$46080$	$1.113255$	$4913$	$0.79101$	$3.53415$	$1$	$[1, -1, 1, -5180, 116822]$	\(y^2+xy+y=x^3-x^2-5180x+116822\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
38025.ck2	38025cs1	38025.ck	38025cs	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 5^{9} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$599040$	$2.395729$	$4913$	$0.79101$	$4.99344$	$1$	$[1, -1, 0, -875367, 254032416]$	\(y^2+xy=x^3-x^2-875367x+254032416\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
38025.cl2	38025cr1	38025.cl	38025cr	$2$	$2$	\( 3^{2} \cdot 5^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 5^{3} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$9216$	$0.308536$	$4913$	$0.79101$	$2.61848$	$1$	$[1, -1, 0, -207, 976]$	\(y^2+xy=x^3-x^2-207x+976\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
67600.o2	67600dm1	67600.o	67600dm	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{12} \cdot 5^{3} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$319488$	$1.734852$	$4913$	$0.79101$	$4.02201$	$1$	$[0, 1, 0, -62248, 4792308]$	\(y^2=x^3+x^2-62248x+4792308\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
67600.p2	67600dl1	67600.p	67600dl	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{12} \cdot 5^{3} \cdot 13^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1.339361760$	$1$		$15$	$24576$	$0.452377$	$4913$	$0.79101$	$2.63822$	$1$	$[0, 1, 0, -368, 2068]$	\(y^2=x^3+x^2-368x+2068\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(4, 26), (-6, 64)]$	$1$
67600.cy2	67600di1	67600.cy	67600di	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{12} \cdot 5^{9} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$4$	$2$	$1$	$1597440$	$2.539570$	$4913$	$0.79101$	$4.89031$	$1$	$[0, -1, 0, -1556208, 602150912]$	\(y^2=x^3-x^2-1556208x+602150912\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
67600.dc2	67600dh1	67600.dc	67600dh	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{12} \cdot 5^{9} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$122880$	$1.257095$	$4913$	$0.79101$	$3.50651$	$1$	$[0, -1, 0, -9208, 276912]$	\(y^2=x^3-x^2-9208x+276912\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
207025.q2	207025q1	207025.q	207025q	$2$	$2$	\( 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 7^{6} \cdot 13^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$21840$	$1152$	$41$	$1.136010295$	$1$		$19$	$147456$	$0.732184$	$4913$	$0.79101$	$2.67130$	$1$	$[1, 0, 0, -1128, 11647]$	\(y^2+xy=x^3-1128x+11647\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-3, 124), (11, 19)]$	$1$
207025.bf2	207025bf1	207025.bf	207025bf	$2$	$2$	\( 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 7^{6} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$21840$	$1152$	$41$	$1$	$4$	$2$	$1$	$9584640$	$2.819378$	$4913$	$0.79101$	$4.71747$	$1$	$[1, 1, 1, -4765888, 3222386656]$	\(y^2+xy+y=x^3+x^2-4765888x+3222386656\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
207025.bu2	207025bt1	207025.bu	207025bt	$2$	$2$	\( 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 5^{3} \cdot 7^{6} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$21840$	$1152$	$41$	$1$	$1$		$1$	$1916928$	$2.014660$	$4913$	$0.79101$	$3.92856$	$1$	$[1, 0, 1, -190636, 25779093]$	\(y^2+xy+y=x^3-190636x+25779093\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
207025.cj2	207025cj1	207025.cj	207025cj	$2$	$2$	\( 5^{2} \cdot 7^{2} \cdot 13^{2} \)	\( 5^{9} \cdot 7^{6} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$21840$	$1152$	$41$	$1$	$1$		$1$	$737280$	$1.536903$	$4913$	$0.79101$	$3.46020$	$1$	$[1, 1, 0, -28200, 1455875]$	\(y^2+xy=x^3+x^2-28200x+1455875\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
270400.bn2	270400bn1	270400.bn	270400bn	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{9} \cdot 13^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$5.464613703$	$1$		$11$	$983040$	$1.603670$	$4913$	$0.79101$	$3.45037$	$1$	$[0, 1, 0, -36833, 2178463]$	\(y^2=x^3+x^2-36833x+2178463\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(33, 1000), (39, 896)]$	$1$
270400.bo2	270400bo1	270400.bo	270400bo	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{3} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$4.919284545$	$1$		$3$	$2555904$	$2.081425$	$4913$	$0.79101$	$3.90874$	$1$	$[0, 1, 0, -248993, -38587457]$	\(y^2=x^3+x^2-248993x-38587457\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(819, 17536)]$	$1$
270400.bt2	270400bt1	270400.bt	270400bt	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{3} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1.389203272$	$1$		$7$	$196608$	$0.798950$	$4913$	$0.79101$	$2.67832$	$1$	$[0, 1, 0, -1473, -18017]$	\(y^2=x^3+x^2-1473x-18017\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-22, 65)]$	$1$
270400.bu2	270400bu1	270400.bu	270400bu	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{9} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$12779520$	$2.886143$	$4913$	$0.79101$	$4.68079$	$1$	$[0, 1, 0, -6224833, 4810982463]$	\(y^2=x^3+x^2-6224833x+4810982463\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
270400.is2	270400is1	270400.is	270400is	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{3} \cdot 13^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$1$		$1$	$196608$	$0.798950$	$4913$	$0.79101$	$2.67832$	$1$	$[0, -1, 0, -1473, 18017]$	\(y^2=x^3-x^2-1473x+18017\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$
270400.it2	270400it1	270400.it	270400it	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{9} \cdot 13^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$32.20739928$	$1$		$1$	$12779520$	$2.886143$	$4913$	$0.79101$	$4.68079$	$1$	$[0, -1, 0, -6224833, -4810982463]$	\(y^2=x^3-x^2-6224833x-4810982463\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(-378616990921119/624721, 4319828329162222909248/624721)]$	$1$
270400.iz2	270400iz1	270400.iz	270400iz	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{9} \cdot 13^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$8.578872281$	$1$		$1$	$983040$	$1.603670$	$4913$	$0.79101$	$3.45037$	$1$	$[0, -1, 0, -36833, -2178463]$	\(y^2=x^3-x^2-36833x-2178463\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[(33961/9, 5450752/9)]$	$1$
270400.ja2	270400ja1	270400.ja	270400ja	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 13^{2} \)	\( 2^{18} \cdot 5^{3} \cdot 13^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2, 3$	16.24.0.21, 3.3.0.1	2B, 3Nn	$3120$	$1152$	$41$	$1$	$4$	$2$	$1$	$2555904$	$2.081425$	$4913$	$0.79101$	$3.90874$	$1$	$[0, -1, 0, -248993, 38587457]$	\(y^2=x^3-x^2-248993x+38587457\)	2.3.0.a.1, 3.3.0.a.1, 4.6.0.d.1, 6.9.0.a.1, 8.12.0.w.1, $\ldots$	$[ ]$	$1$

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