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

Sort order

Select

Results (32 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
1710.a2	1710a1	1710.a	1710a	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.853993447$	$1$		$9$	$1920$	$0.607739$	$961504803/486400$	$[1, -1, 0, -555, 1925]$	\(y^2+xy=x^3-x^2-555x+1925\)
1710.p2	1710m1	1710.p	1710m	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.216414238$	$1$		$13$	$640$	$0.058433$	$961504803/486400$	$[1, -1, 1, -62, -51]$	\(y^2+xy+y=x^3-x^2-62x-51\)
8550.q2	8550b1	8550.q	8550b	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.086084476$	$1$		$5$	$15360$	$0.863152$	$961504803/486400$	$[1, -1, 0, -1542, -7884]$	\(y^2+xy=x^3-x^2-1542x-7884\)
8550.bl2	8550t1	8550.bl	8550t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$46080$	$1.412458$	$961504803/486400$	$[1, -1, 1, -13880, 226747]$	\(y^2+xy+y=x^3-x^2-13880x+226747\)
13680.z2	13680w1	13680.z	13680w	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{9} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.252337760$	$1$		$5$	$46080$	$1.300886$	$961504803/486400$	$[0, 0, 0, -8883, -114318]$	\(y^2=x^3-8883x-114318\)
13680.bw2	13680y1	13680.bw	13680y	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{22} \cdot 3^{3} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$15360$	$0.751580$	$961504803/486400$	$[0, 0, 0, -987, 4234]$	\(y^2=x^3-987x+4234\)
32490.l2	32490g1	32490.l	32490g	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.843084840$	$1$		$9$	$230400$	$1.530653$	$961504803/486400$	$[1, -1, 0, -22269, 459333]$	\(y^2+xy=x^3-x^2-22269x+459333\)
32490.bd2	32490bd1	32490.bd	32490bd	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.769652213$	$1$		$9$	$691200$	$2.079960$	$961504803/486400$	$[1, -1, 1, -200423, -12201569]$	\(y^2+xy+y=x^3-x^2-200423x-12201569\)
54720.f2	54720g1	54720.f	54720g	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{28} \cdot 3^{3} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$122880$	$1.098154$	$961504803/486400$	$[0, 0, 0, -3948, -33872]$	\(y^2=x^3-3948x-33872\)
54720.cg2	54720cu1	54720.cg	54720cu	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{28} \cdot 3^{3} \cdot 5^{2} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$122880$	$1.098154$	$961504803/486400$	$[0, 0, 0, -3948, 33872]$	\(y^2=x^3-3948x+33872\)
54720.cm2	54720n1	54720.cm	54720n	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{28} \cdot 3^{9} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$2.529354511$	$1$		$5$	$368640$	$1.647459$	$961504803/486400$	$[0, 0, 0, -35532, 914544]$	\(y^2=x^3-35532x+914544\)
54720.fd2	54720dd1	54720.fd	54720dd	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 19 \)	\( 2^{28} \cdot 3^{9} \cdot 5^{2} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$5.822009695$	$1$		$1$	$368640$	$1.647459$	$961504803/486400$	$[0, 0, 0, -35532, -914544]$	\(y^2=x^3-35532x-914544\)
68400.g2	68400do1	68400.g	68400do	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{9} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$4.752737149$	$1$		$5$	$1105920$	$2.105606$	$961504803/486400$	$[0, 0, 0, -222075, -14289750]$	\(y^2=x^3-222075x-14289750\)
68400.q2	68400dn1	68400.q	68400dn	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{22} \cdot 3^{3} \cdot 5^{8} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3.007574384$	$1$		$5$	$368640$	$1.556299$	$961504803/486400$	$[0, 0, 0, -24675, 529250]$	\(y^2=x^3-24675x+529250\)
83790.cp2	83790t1	83790.cp	83790t	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 7^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$552960$	$1.580694$	$961504803/486400$	$[1, -1, 0, -27204, -605872]$	\(y^2+xy=x^3-x^2-27204x-605872\)
83790.cr2	83790cz1	83790.cr	83790cz	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$0.494584030$	$1$		$31$	$184320$	$1.031387$	$961504803/486400$	$[1, -1, 1, -3023, 23447]$	\(y^2+xy+y=x^3-x^2-3023x+23447\)
162450.ck2	162450ez1	162450.ck	162450ez	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{9} \cdot 5^{8} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$16588800$	$2.884678$	$961504803/486400$	$[1, -1, 0, -5010567, -1530206659]$	\(y^2+xy=x^3-x^2-5010567x-1530206659\)
162450.eu2	162450ck1	162450.eu	162450ck	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{3} \cdot 5^{8} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.561130466$	$1$		$7$	$5529600$	$2.335373$	$961504803/486400$	$[1, -1, 1, -556730, 56859897]$	\(y^2+xy+y=x^3-x^2-556730x+56859897\)
206910.cr2	206910fa1	206910.cr	206910fa	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$691200$	$1.257380$	$961504803/486400$	$[1, -1, 0, -7464, 89920]$	\(y^2+xy=x^3-x^2-7464x+89920\)
206910.dv2	206910cm1	206910.dv	206910cm	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 11^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2073600$	$1.806686$	$961504803/486400$	$[1, -1, 1, -67178, -2360663]$	\(y^2+xy+y=x^3-x^2-67178x-2360663\)
259920.dj2	259920dj1	259920.dj	259920dj	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{22} \cdot 3^{9} \cdot 5^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6.066476207$	$1$		$1$	$16588800$	$2.773106$	$961504803/486400$	$[0, 0, 0, -3206763, 784107162]$	\(y^2=x^3-3206763x+784107162\)
259920.gx2	259920gx1	259920.gx	259920gx	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 19^{2} \)	\( 2^{22} \cdot 3^{3} \cdot 5^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$5529600$	$2.223801$	$961504803/486400$	$[0, 0, 0, -356307, -29041006]$	\(y^2=x^3-356307x-29041006\)
273600.n2	273600n1	273600.n	273600n	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{28} \cdot 3^{3} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$2949120$	$1.902872$	$961504803/486400$	$[0, 0, 0, -98700, 4234000]$	\(y^2=x^3-98700x+4234000\)
273600.cg2	273600cg1	273600.cg	273600cg	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{28} \cdot 3^{9} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$8847360$	$2.452179$	$961504803/486400$	$[0, 0, 0, -888300, -114318000]$	\(y^2=x^3-888300x-114318000\)
273600.og2	273600og1	273600.og	273600og	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{28} \cdot 3^{9} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$8847360$	$2.452179$	$961504803/486400$	$[0, 0, 0, -888300, 114318000]$	\(y^2=x^3-888300x+114318000\)
273600.qa2	273600qa1	273600.qa	273600qa	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 19 \)	\( 2^{28} \cdot 3^{3} \cdot 5^{8} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$4$	$2$	$1$	$2949120$	$1.902872$	$961504803/486400$	$[0, 0, 0, -98700, -4234000]$	\(y^2=x^3-98700x-4234000\)
288990.cb2	288990cb1	288990.cb	288990cb	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 13^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$1505280$	$1.340908$	$961504803/486400$	$[1, -1, 0, -10425, -142739]$	\(y^2+xy=x^3-x^2-10425x-142739\)
288990.gz2	288990gz1	288990.gz	288990gz	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 13^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$4515840$	$1.890213$	$961504803/486400$	$[1, -1, 1, -93827, 3947779]$	\(y^2+xy+y=x^3-x^2-93827x+3947779\)
418950.f2	418950f1	418950.f	418950f	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1.924916293$	$1$		$7$	$4423680$	$1.836107$	$961504803/486400$	$[1, -1, 0, -75567, 2855341]$	\(y^2+xy=x^3-x^2-75567x+2855341\)
418950.qx2	418950qx1	418950.qx	418950qx	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$13271040$	$2.385414$	$961504803/486400$	$[1, -1, 1, -680105, -76414103]$	\(y^2+xy+y=x^3-x^2-680105x-76414103\)
494190.cs2	494190cs1	494190.cs	494190cs	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{9} \cdot 5^{2} \cdot 17^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$9461760$	$2.024345$	$961504803/486400$	$[1, -1, 0, -160449, 8815805]$	\(y^2+xy=x^3-x^2-160449x+8815805\)
494190.el2	494190el1	494190.el	494190el	$2$	$2$	\( 2 \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{3} \cdot 5^{2} \cdot 17^{6} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$1$	$1$		$1$	$3153920$	$1.475040$	$961504803/486400$	$[1, -1, 1, -17828, -320569]$	\(y^2+xy+y=x^3-x^2-17828x-320569\)