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 (17 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
4830.n2	4830n2	4830.n	4830n	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$1$	$1$		$2$	$645120$	$3.061157$	$16077778198622525072705635801/388799208512064000000$	$[1, 0, 1, -52581638, -146758467112]$	\(y^2+xy+y=x^3-52581638x-146758467112\)
14490.bg2	14490bl2	14490.bg	14490bl	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{20} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$3.013608008$	$1$		$8$	$5160960$	$3.610462$	$16077778198622525072705635801/388799208512064000000$	$[1, -1, 1, -473234738, 3962478612017]$	\(y^2+xy+y=x^3-x^2-473234738x+3962478612017\)
24150.by2	24150bt2	24150.by	24150bt	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{14} \cdot 5^{12} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$5.955132340$	$1$		$4$	$15482880$	$3.865875$	$16077778198622525072705635801/388799208512064000000$	$[1, 1, 1, -1314540938, -18344808388969]$	\(y^2+xy+y=x^3+x^2-1314540938x-18344808388969\)
33810.l2	33810l2	33810.l	33810l	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{12} \cdot 3^{14} \cdot 5^{6} \cdot 7^{10} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$12.46399861$	$1$		$2$	$30965760$	$4.034111$	$16077778198622525072705635801/388799208512064000000$	$[1, 1, 0, -2576500238, 50335577719092]$	\(y^2+xy=x^3+x^2-2576500238x+50335577719092\)
38640.bl2	38640ca2	38640.bl	38640ca	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$3$	$15482880$	$3.754303$	$16077778198622525072705635801/388799208512064000000$	$[0, -1, 0, -841306200, 9392541895152]$	\(y^2=x^3-x^2-841306200x+9392541895152\)
72450.bi2	72450bv2	72450.bi	72450bv	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{12} \cdot 3^{20} \cdot 5^{12} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$123863040$	$4.415184$	$16077778198622525072705635801/388799208512064000000$	$[1, -1, 0, -11830868442, 495297995633716]$	\(y^2+xy=x^3-x^2-11830868442x+495297995633716\)
101430.eh2	101430fa2	101430.eh	101430fa	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{12} \cdot 3^{20} \cdot 5^{6} \cdot 7^{10} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$5.568928548$	$1$		$6$	$247726080$	$4.583420$	$16077778198622525072705635801/388799208512064000000$	$[1, -1, 1, -23188502147, -1359083786917629]$	\(y^2+xy+y=x^3-x^2-23188502147x-1359083786917629\)
111090.z2	111090ba2	111090.z	111090ba	$4$	$4$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{12} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$340623360$	$4.628906$	$16077778198622525072705635801/388799208512064000000$	$[1, 0, 1, -27815686249, 1785554637976172]$	\(y^2+xy+y=x^3-27815686249x+1785554637976172\)
115920.ch2	115920dv2	115920.ch	115920dv	$4$	$4$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{20} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$30.71791485$	$1$		$3$	$123863040$	$4.303612$	$16077778198622525072705635801/388799208512064000000$	$[0, 0, 0, -7571755803, -253591059413302]$	\(y^2=x^3-7571755803x-253591059413302\)
154560.c2	154560hs2	154560.c	154560hs	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$123863040$	$4.100876$	$16077778198622525072705635801/388799208512064000000$	$[0, -1, 0, -3365224801, -75136969936415]$	\(y^2=x^3-x^2-3365224801x-75136969936415\)
154560.fz2	154560bo2	154560.fz	154560bo	$4$	$4$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{14} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.1	2Cs	$1$	$1$		$3$	$123863040$	$4.100876$	$16077778198622525072705635801/388799208512064000000$	$[0, 1, 0, -3365224801, 75136969936415]$	\(y^2=x^3+x^2-3365224801x+75136969936415\)
169050.jc2	169050bz2	169050.jc	169050bz	$4$	$4$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{12} \cdot 3^{14} \cdot 5^{12} \cdot 7^{10} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$2$	$743178240$	$4.838829$	$16077778198622525072705635801/388799208512064000000$	$[1, 0, 0, -64412505963, 6292076039898417]$	\(y^2+xy=x^3-64412505963x+6292076039898417\)
193200.ds2	193200bx2	193200.ds	193200bx	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{24} \cdot 3^{14} \cdot 5^{12} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$1$		$3$	$371589120$	$4.559021$	$16077778198622525072705635801/388799208512064000000$	$[0, 1, 0, -21032655008, 1174025671583988]$	\(y^2=x^3+x^2-21032655008x+1174025671583988\)
270480.fa2	270480fa2	270480.fa	270480fa	$4$	$4$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{24} \cdot 3^{14} \cdot 5^{6} \cdot 7^{10} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$1$		$3$	$743178240$	$4.727257$	$16077778198622525072705635801/388799208512064000000$	$[0, 1, 0, -41224003816, -3221559422029516]$	\(y^2=x^3+x^2-41224003816x-3221559422029516\)
333270.fc2	333270fc2	333270.fc	333270fc	$4$	$4$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{12} \cdot 3^{20} \cdot 5^{6} \cdot 7^{4} \cdot 23^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.1	2Cs	$1$	$4$	$2$	$2$	$2724986880$	$5.178207$	$16077778198622525072705635801/388799208512064000000$	$[1, -1, 1, -250341176237, -48209975225356651]$	\(y^2+xy+y=x^3-x^2-250341176237x-48209975225356651\)
463680.ke2	463680ke2	463680.ke	463680ke	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{20} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$10.48398181$	$1$		$3$	$990904320$	$4.650185$	$16077778198622525072705635801/388799208512064000000$	$[0, 0, 0, -30287023212, 2028728475306416]$	\(y^2=x^3-30287023212x+2028728475306416\)
463680.lc2	463680lc2	463680.lc	463680lc	$4$	$4$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{30} \cdot 3^{20} \cdot 5^{6} \cdot 7^{4} \cdot 23^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.6.0.1	2Cs	$1$	$4$	$2$	$3$	$990904320$	$4.650185$	$16077778198622525072705635801/388799208512064000000$	$[0, 0, 0, -30287023212, -2028728475306416]$	\(y^2=x^3-30287023212x-2028728475306416\)