Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (40 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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
2400.c1	2400y2	2400.c	2400y	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.703050583$	$1$		$9$	$384$	$-0.133183$	$195112/9$	$[0, -1, 0, -48, -108]$	\(y^2=x^3-x^2-48x-108\)
2400.d1	2400e2	2400.d	2400e	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1920$	$0.671536$	$195112/9$	$[0, -1, 0, -1208, 15912]$	\(y^2=x^3-x^2-1208x+15912\)
2400.be1	2400o2	2400.be	2400o	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.278967272$	$1$		$5$	$1920$	$0.671536$	$195112/9$	$[0, 1, 0, -1208, -15912]$	\(y^2=x^3+x^2-1208x-15912\)
2400.bf1	2400bf2	2400.bf	2400bf	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$384$	$-0.133183$	$195112/9$	$[0, 1, 0, -48, 108]$	\(y^2=x^3+x^2-48x+108\)
4800.z1	4800bt2	4800.z	4800bt	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.400252180$	$1$		$11$	$1536$	$0.213391$	$195112/9$	$[0, -1, 0, -193, 1057]$	\(y^2=x^3-x^2-193x+1057\)
4800.ba1	4800bs2	4800.ba	4800bs	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.573345757$	$1$		$5$	$7680$	$1.018110$	$195112/9$	$[0, -1, 0, -4833, -122463]$	\(y^2=x^3-x^2-4833x-122463\)
4800.bt1	4800cn2	4800.bt	4800cn	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$7680$	$1.018110$	$195112/9$	$[0, 1, 0, -4833, 122463]$	\(y^2=x^3+x^2-4833x+122463\)
4800.bu1	4800cm2	4800.bu	4800cm	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1536$	$0.213391$	$195112/9$	$[0, 1, 0, -193, -1057]$	\(y^2=x^3+x^2-193x-1057\)
7200.j1	7200bv2	7200.j	7200bv	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$15360$	$1.220842$	$195112/9$	$[0, 0, 0, -10875, -418750]$	\(y^2=x^3-10875x-418750\)
7200.p1	7200w2	7200.p	7200w	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.627702952$	$1$		$7$	$3072$	$0.416123$	$195112/9$	$[0, 0, 0, -435, 3350]$	\(y^2=x^3-435x+3350\)
7200.bl1	7200v2	7200.bl	7200v	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.987912800$	$1$		$3$	$3072$	$0.416123$	$195112/9$	$[0, 0, 0, -435, -3350]$	\(y^2=x^3-435x-3350\)
7200.br1	7200bt2	7200.br	7200bt	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$15360$	$1.220842$	$195112/9$	$[0, 0, 0, -10875, 418750]$	\(y^2=x^3-10875x+418750\)
14400.bc1	14400ez2	14400.bc	14400ez	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{3} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.669406797$	$1$		$25$	$12288$	$0.762697$	$195112/9$	$[0, 0, 0, -1740, 26800]$	\(y^2=x^3-1740x+26800\)
14400.bw1	14400ey2	14400.bw	14400ey	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$61440$	$1.567415$	$195112/9$	$[0, 0, 0, -43500, -3350000]$	\(y^2=x^3-43500x-3350000\)
14400.dp1	14400es2	14400.dp	14400es	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$61440$	$1.567415$	$195112/9$	$[0, 0, 0, -43500, 3350000]$	\(y^2=x^3-43500x+3350000\)
14400.ej1	14400er2	14400.ej	14400er	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$12288$	$0.762697$	$195112/9$	$[0, 0, 0, -1740, -26800]$	\(y^2=x^3-1740x-26800\)
117600.f1	117600cc2	117600.f	117600cc	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.565211092$	$1$		$5$	$691200$	$1.644491$	$195112/9$	$[0, -1, 0, -59208, 5339412]$	\(y^2=x^3-x^2-59208x+5339412\)
117600.dx1	117600gd2	117600.dx	117600gd	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$138240$	$0.839772$	$195112/9$	$[0, -1, 0, -2368, -41768]$	\(y^2=x^3-x^2-2368x-41768\)
117600.ee1	117600ig2	117600.ee	117600ig	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.534442305$	$1$		$5$	$138240$	$0.839772$	$195112/9$	$[0, 1, 0, -2368, 41768]$	\(y^2=x^3+x^2-2368x+41768\)
117600.ih1	117600ed2	117600.ih	117600ed	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$9$	$3$	$1$	$691200$	$1.644491$	$195112/9$	$[0, 1, 0, -59208, -5339412]$	\(y^2=x^3+x^2-59208x-5339412\)
235200.i1	235200i2	235200.i	235200i	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2764800$	$1.991064$	$195112/9$	$[0, -1, 0, -236833, -42478463]$	\(y^2=x^3-x^2-236833x-42478463\)
235200.oe1	235200oe2	235200.oe	235200oe	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$552960$	$1.186346$	$195112/9$	$[0, -1, 0, -9473, 343617]$	\(y^2=x^3-x^2-9473x+343617\)
235200.oz1	235200oz2	235200.oz	235200oz	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{3} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.659175694$	$1$		$5$	$552960$	$1.186346$	$195112/9$	$[0, 1, 0, -9473, -343617]$	\(y^2=x^3+x^2-9473x-343617\)
235200.bco1	235200bco2	235200.bco	235200bco	$2$	$2$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{2} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4.363173500$	$1$		$3$	$2764800$	$1.991064$	$195112/9$	$[0, 1, 0, -236833, 42478463]$	\(y^2=x^3+x^2-236833x+42478463\)
290400.cs1	290400cs2	290400.cs	290400cs	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.772727916$	$1$		$7$	$414720$	$1.065765$	$195112/9$	$[0, -1, 0, -5848, 167092]$	\(y^2=x^3-x^2-5848x+167092\)
290400.da1	290400da2	290400.da	290400da	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$9$	$3$	$1$	$2073600$	$1.870483$	$195112/9$	$[0, -1, 0, -146208, -20594088]$	\(y^2=x^3-x^2-146208x-20594088\)
290400.ei1	290400ei2	290400.ei	290400ei	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$414720$	$1.065765$	$195112/9$	$[0, 1, 0, -5848, -167092]$	\(y^2=x^3+x^2-5848x-167092\)
290400.eq1	290400eq2	290400.eq	290400eq	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 11^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.513057602$	$1$		$3$	$2073600$	$1.870483$	$195112/9$	$[0, 1, 0, -146208, 20594088]$	\(y^2=x^3+x^2-146208x+20594088\)
352800.f1	352800f2	352800.f	352800f	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1105920$	$1.389078$	$195112/9$	$[0, 0, 0, -21315, 1149050]$	\(y^2=x^3-21315x+1149050\)
352800.k1	352800k2	352800.k	352800k	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4.430545041$	$1$		$3$	$5529600$	$2.193798$	$195112/9$	$[0, 0, 0, -532875, 143631250]$	\(y^2=x^3-532875x+143631250\)
352800.ot1	352800ot2	352800.ot	352800ot	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{3} \cdot 7^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1105920$	$1.389078$	$195112/9$	$[0, 0, 0, -21315, -1149050]$	\(y^2=x^3-21315x-1149050\)
352800.oy1	352800oy2	352800.oy	352800oy	$2$	$2$	\( 2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{9} \cdot 3^{8} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6.901921317$	$1$		$1$	$5529600$	$2.193798$	$195112/9$	$[0, 0, 0, -532875, -143631250]$	\(y^2=x^3-532875x-143631250\)
405600.cs1	405600cs2	405600.cs	405600cs	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.840515317$	$1$		$3$	$4423680$	$1.954012$	$195112/9$	$[0, -1, 0, -204208, 34141912]$	\(y^2=x^3-x^2-204208x+34141912\)
405600.db1	405600db2	405600.db	405600db	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$884736$	$1.149292$	$195112/9$	$[0, -1, 0, -8168, -269868]$	\(y^2=x^3-x^2-8168x-269868\)
405600.ef1	405600ef2	405600.ef	405600ef	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{3} \cdot 13^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.367337459$	$1$		$3$	$884736$	$1.149292$	$195112/9$	$[0, 1, 0, -8168, 269868]$	\(y^2=x^3+x^2-8168x+269868\)
405600.en1	405600en2	405600.en	405600en	$2$	$2$	\( 2^{5} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)	\( 2^{9} \cdot 3^{2} \cdot 5^{9} \cdot 13^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$4423680$	$1.954012$	$195112/9$	$[0, 1, 0, -204208, -34141912]$	\(y^2=x^3+x^2-204208x-34141912\)
705600.q1	-	705600.q	-	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6.266476325$	$1$		$3$	$22118400$	$2.540371$	$195112/9$	$[0, 0, 0, -2131500, -1149050000]$	\(y^2=x^3-2131500x-1149050000\)
705600.bo1	-	705600.bo	-	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.937943525$	$1$		$7$	$4423680$	$1.735653$	$195112/9$	$[0, 0, 0, -85260, -9192400]$	\(y^2=x^3-85260x-9192400\)
705600.cbe1	-	705600.cbe	-	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{9} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.176588014$	$1$		$7$	$22118400$	$2.540371$	$195112/9$	$[0, 0, 0, -2131500, 1149050000]$	\(y^2=x^3-2131500x+1149050000\)
705600.ccc1	-	705600.ccc	-	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \)	\( 2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.289320885$	$1$		$3$	$4423680$	$1.735653$	$195112/9$	$[0, 0, 0, -85260, 9192400]$	\(y^2=x^3-85260x+9192400\)