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
825.b1	825a1	825.b	825a	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.267281464$	$1$		$4$	$72$	$-0.301211$	$-56197120/3267$	$[0, -1, 1, -23, 53]$	\(y^2+y=x^3-x^2-23x+53\)
825.c1	825c1	825.c	825c	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$0.750802424$	$1$		$8$	$360$	$0.503509$	$-56197120/3267$	$[0, 1, 1, -583, 5494]$	\(y^2+y=x^3+x^2-583x+5494\)
2475.e1	2475k1	2475.e	2475k	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$1$	$1$		$0$	$2880$	$1.052814$	$-56197120/3267$	$[0, 0, 1, -5250, -153594]$	\(y^2+y=x^3-5250x-153594\)
2475.f1	2475i1	2475.f	2475i	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.553485365$	$1$		$4$	$576$	$0.248095$	$-56197120/3267$	$[0, 0, 1, -210, -1229]$	\(y^2+y=x^3-210x-1229\)
9075.i1	9075f1	9075.i	9075f	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$8640$	$0.897737$	$-56197120/3267$	$[0, -1, 1, -2823, -59632]$	\(y^2+y=x^3-x^2-2823x-59632\)
9075.l1	9075t1	9075.l	9075t	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$43200$	$1.702456$	$-56197120/3267$	$[0, 1, 1, -70583, -7595131]$	\(y^2+y=x^3+x^2-70583x-7595131\)
13200.y1	13200by1	13200.y	13200by	$2$	$3$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$25920$	$1.196655$	$-56197120/3267$	$[0, -1, 0, -9333, -360963]$	\(y^2=x^3-x^2-9333x-360963\)
13200.cd1	13200ch1	13200.cd	13200ch	$2$	$3$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$5184$	$0.391936$	$-56197120/3267$	$[0, 1, 0, -373, -3037]$	\(y^2=x^3+x^2-373x-3037\)
27225.y1	27225bg1	27225.y	27225bg	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.925551758$	$1$		$4$	$69120$	$1.447042$	$-56197120/3267$	$[0, 0, 1, -25410, 1635466]$	\(y^2+y=x^3-25410x+1635466\)
27225.bc1	27225bz1	27225.bc	27225bz	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 3^{9} \cdot 5^{8} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$345600$	$2.251762$	$-56197120/3267$	$[0, 0, 1, -635250, 204433281]$	\(y^2+y=x^3-635250x+204433281\)
39600.cc1	39600da1	39600.cc	39600da	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.389262744$	$1$		$2$	$41472$	$0.941242$	$-56197120/3267$	$[0, 0, 0, -3360, 78640]$	\(y^2=x^3-3360x+78640\)
39600.dg1	39600ei1	39600.dg	39600ei	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$207360$	$1.745962$	$-56197120/3267$	$[0, 0, 0, -84000, 9830000]$	\(y^2=x^3-84000x+9830000\)
40425.bi1	40425bd1	40425.bi	40425bd	$2$	$3$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$12.08117933$	$1$		$0$	$136080$	$1.476463$	$-56197120/3267$	$[0, -1, 1, -28583, -1941682]$	\(y^2+y=x^3-x^2-28583x-1941682\)
40425.bt1	40425ca1	40425.bt	40425ca	$2$	$3$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.147301605$	$1$		$4$	$27216$	$0.671744$	$-56197120/3267$	$[0, 1, 1, -1143, -15991]$	\(y^2+y=x^3+x^2-1143x-15991\)
52800.br1	52800ed1	52800.br	52800ed	$2$	$3$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$10368$	$0.045363$	$-56197120/3267$	$[0, -1, 0, -93, -333]$	\(y^2=x^3-x^2-93x-333\)
52800.bw1	52800bs1	52800.bw	52800bs	$2$	$3$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.350081924$	$1$		$2$	$51840$	$0.850081$	$-56197120/3267$	$[0, -1, 0, -2333, 46287]$	\(y^2=x^3-x^2-2333x+46287\)
52800.fy1	52800hi1	52800.fy	52800hi	$2$	$3$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{3} \cdot 5^{8} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$51840$	$0.850081$	$-56197120/3267$	$[0, 1, 0, -2333, -46287]$	\(y^2=x^3+x^2-2333x-46287\)
52800.gf1	52800cs1	52800.gf	52800cs	$2$	$3$	\( 2^{6} \cdot 3 \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{3} \cdot 5^{2} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.603675125$	$1$		$2$	$10368$	$0.045363$	$-56197120/3267$	$[0, 1, 0, -93, 333]$	\(y^2=x^3+x^2-93x+333\)
121275.dw1	121275dt1	121275.dw	121275dt	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 3^{9} \cdot 5^{2} \cdot 7^{6} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$217728$	$1.221050$	$-56197120/3267$	$[0, 0, 1, -10290, 421461]$	\(y^2+y=x^3-10290x+421461\)
121275.dy1	121275gi1	121275.dy	121275gi	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 11 \)	\( - 3^{9} \cdot 5^{8} \cdot 7^{6} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.706055821$	$1$		$4$	$1088640$	$2.025768$	$-56197120/3267$	$[0, 0, 1, -257250, 52682656]$	\(y^2+y=x^3-257250x+52682656\)
139425.r1	139425be1	139425.r	139425be	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$168480$	$0.981264$	$-56197120/3267$	$[0, -1, 1, -3943, 101298]$	\(y^2+y=x^3-x^2-3943x+101298\)
139425.be1	139425u1	139425.be	139425u	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$842400$	$1.785982$	$-56197120/3267$	$[0, 1, 1, -98583, 12465119]$	\(y^2+y=x^3+x^2-98583x+12465119\)
145200.ch1	145200dv1	145200.ch	145200dv	$2$	$3$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{8} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$3110400$	$2.395603$	$-56197120/3267$	$[0, -1, 0, -1129333, 484959037]$	\(y^2=x^3-x^2-1129333x+484959037\)
145200.iu1	145200cl1	145200.iu	145200cl	$2$	$3$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$622080$	$1.590883$	$-56197120/3267$	$[0, 1, 0, -45173, 3861603]$	\(y^2=x^3+x^2-45173x+3861603\)
158400.fl1	158400is1	158400.fl	158400is	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.490512628$	$1$		$2$	$414720$	$1.399387$	$-56197120/3267$	$[0, 0, 0, -21000, -1228750]$	\(y^2=x^3-21000x-1228750\)
158400.fw1	158400dm1	158400.fw	158400dm	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.126835681$	$1$		$6$	$82944$	$0.594669$	$-56197120/3267$	$[0, 0, 0, -840, 9830]$	\(y^2=x^3-840x+9830\)
158400.jd1	158400md1	158400.jd	158400md	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{9} \cdot 5^{2} \cdot 11^{2} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$82944$	$0.594669$	$-56197120/3267$	$[0, 0, 0, -840, -9830]$	\(y^2=x^3-840x-9830\)
158400.jx1	158400bh1	158400.jx	158400bh	$2$	$3$	\( 2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( - 2^{6} \cdot 3^{9} \cdot 5^{8} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1.143839133$	$1$		$2$	$414720$	$1.399387$	$-56197120/3267$	$[0, 0, 0, -21000, 1228750]$	\(y^2=x^3-21000x+1228750\)
238425.be1	238425be1	238425.be	238425be	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \cdot 17^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$2.963224666$	$1$		$2$	$1658880$	$1.920115$	$-56197120/3267$	$[0, -1, 1, -168583, 28004568]$	\(y^2+y=x^3-x^2-168583x+28004568\)
238425.bn1	238425bn1	238425.bn	238425bn	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 17^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \cdot 17^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$0.812136603$	$1$		$4$	$331776$	$1.115396$	$-56197120/3267$	$[0, 1, 1, -6743, 221339]$	\(y^2+y=x^3+x^2-6743x+221339\)
297825.bf1	297825bf1	297825.bf	297825bf	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 19^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7.123475377$	$1$		$2$	$2274480$	$1.975727$	$-56197120/3267$	$[0, -1, 1, -210583, -38948307]$	\(y^2+y=x^3-x^2-210583x-38948307\)
297825.bm1	297825bm1	297825.bm	297825bm	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 19^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \cdot 19^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$5.987322889$	$1$		$0$	$454896$	$1.171009$	$-56197120/3267$	$[0, 1, 1, -8423, -314956]$	\(y^2+y=x^3+x^2-8423x-314956\)
418275.bh1	418275bh1	418275.bh	418275bh	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{9} \cdot 5^{2} \cdot 11^{2} \cdot 13^{6} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$1347840$	$1.530569$	$-56197120/3267$	$[0, 0, 1, -35490, -2699564]$	\(y^2+y=x^3-35490x-2699564\)
418275.bs1	418275bs1	418275.bs	418275bs	$2$	$3$	\( 3^{2} \cdot 5^{2} \cdot 11 \cdot 13^{2} \)	\( - 3^{9} \cdot 5^{8} \cdot 11^{2} \cdot 13^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$8.142783507$	$1$		$0$	$6739200$	$2.335289$	$-56197120/3267$	$[0, 0, 1, -887250, -337445469]$	\(y^2+y=x^3-887250x-337445469\)
435600.ia1	435600ia1	435600.ia	435600ia	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{8} \cdot 11^{8} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$17.73642908$	$1$		$0$	$24883200$	$2.944908$	$-56197120/3267$	$[0, 0, 0, -10164000, -13083730000]$	\(y^2=x^3-10164000x-13083730000\)
435600.mn1	435600mn1	435600.mn	435600mn	$2$	$3$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( - 2^{12} \cdot 3^{9} \cdot 5^{2} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$4976640$	$2.140190$	$-56197120/3267$	$[0, 0, 0, -406560, -104669840]$	\(y^2=x^3-406560x-104669840\)
436425.z1	436425z1	436425.z	436425z	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 23^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \cdot 23^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$3.862842627$	$1$		$0$	$855360$	$1.266537$	$-56197120/3267$	$[0, -1, 1, -12343, -549597]$	\(y^2+y=x^3-x^2-12343x-549597\)
436425.bn1	436425bn1	436425.bn	436425bn	$2$	$3$	\( 3 \cdot 5^{2} \cdot 11 \cdot 23^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \cdot 23^{6} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$7.784912717$	$1$		$0$	$4276800$	$2.071255$	$-56197120/3267$	$[0, 1, 1, -308583, -69316756]$	\(y^2+y=x^3+x^2-308583x-69316756\)
444675.di1	444675di1	444675.di	444675di	$2$	$3$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{8} \cdot 7^{6} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$16329600$	$2.675411$	$-56197120/3267$	$[0, -1, 1, -3458583, 2598212693]$	\(y^2+y=x^3-x^2-3458583x+2598212693\)
444675.es1	444675es1	444675.es	444675es	$2$	$3$	\( 3 \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \)	\( - 3^{3} \cdot 5^{2} \cdot 7^{6} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1$	$1$		$0$	$3265920$	$1.870691$	$-56197120/3267$	$[0, 1, 1, -138343, 20730364]$	\(y^2+y=x^3+x^2-138343x+20730364\)