Elliptic curves over $\Q$ of conductor 4624

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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	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
4624.a1	4624f4	4624.a	4624f	$4$	$6$	\( 2^{4} \cdot 17^{2} \)	\( 2^{13} \cdot 17^{12} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$1$	$82944$	$2.289242$	$159661140625/48275138$	$1.06848$	$6.05679$	$[0, 1, 0, -522608, 100312660]$	\(y^2=x^3+x^2-522608x+100312660\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.8, $\ldots$	$[ ]$
4624.a2	4624f3	4624.a	4624f	$4$	$6$	\( 2^{4} \cdot 17^{2} \)	\( 2^{14} \cdot 17^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$1$	$41472$	$1.942667$	$120920208625/19652$	$0.98564$	$6.02386$	$[0, 1, 0, -476368, 126373524]$	\(y^2=x^3+x^2-476368x+126373524\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 12.24.0-6.a.1.4, $\ldots$	$[ ]$
4624.a3	4624f2	4624.a	4624f	$4$	$6$	\( 2^{4} \cdot 17^{2} \)	\( 2^{15} \cdot 17^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.6, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$1$	$27648$	$1.739935$	$8805624625/2312$	$0.96590$	$5.71343$	$[0, 1, 0, -198928, -34208748]$	\(y^2=x^3+x^2-198928x-34208748\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 12.24.0-6.a.1.2, $\ldots$	$[ ]$
4624.a4	4624f1	4624.a	4624f	$4$	$6$	\( 2^{4} \cdot 17^{2} \)	\( 2^{18} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.6.0.1, 3.4.0.1	2B, 3B	$408$	$96$	$1$	$1$	$1$		$1$	$13824$	$1.393362$	$3048625/1088$	$0.90010$	$4.76919$	$[0, 1, 0, -13968, -398060]$	\(y^2=x^3+x^2-13968x-398060\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 12.24.0-6.a.1.10, $\ldots$	$[ ]$
4624.b1	4624c2	4624.b	4624c	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{10} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.12.0.18	2B	$136$	$48$	$1$	$0.582456720$	$1$		$9$	$1024$	$0.209794$	$1098500$	$0.91788$	$3.47678$	$[0, 1, 0, -368, 2596]$	\(y^2=x^3+x^2-368x+2596\)	2.3.0.a.1, 4.6.0.d.1, 8.12.0.x.1, 34.6.0.a.1, 68.24.0-68.i.1.2, $\ldots$	$[(10, 4)]$
4624.b2	4624c1	4624.b	4624c	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{8} \cdot 17^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.12.0.18	2B	$136$	$48$	$1$	$1.164913441$	$1$		$5$	$512$	$-0.136780$	$2000$	$0.77446$	$2.56496$	$[0, 1, 0, -28, 12]$	\(y^2=x^3+x^2-28x+12\)	2.3.0.a.1, 4.6.0.d.1, 8.12.0.x.1, 34.6.0.a.1, 68.24.0-68.i.1.1, $\ldots$	$[(-2, 8)]$
4624.c1	4624d1	4624.c	4624d	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{8} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.23	2B	$136$	$48$	$0$	$1.565766849$	$1$		$3$	$4608$	$0.808403$	$35152/17$	$0.75928$	$3.91182$	$[0, 1, 0, -1252, -7332]$	\(y^2=x^3+x^2-1252x-7332\)	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.1, 34.6.0.a.1, 68.24.0.f.1, $\ldots$	$[(147, 1734)]$
4624.c2	4624d2	4624.c	4624d	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( - 2^{10} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.12.0.6	2B	$136$	$48$	$0$	$3.131533698$	$1$		$1$	$9216$	$1.154976$	$415292/289$	$0.87236$	$4.36870$	$[0, 1, 0, 4528, -51260]$	\(y^2=x^3+x^2+4528x-51260\)	2.3.0.a.1, 4.12.0-4.a.1.2, 68.24.0-68.d.1.2, 136.48.0.?	$[(197/2, 4335/2)]$
4624.d1	4624e3	4624.d	4624e	$4$	$4$	\( 2^{4} \cdot 17^{2} \)	\( 2^{12} \cdot 17^{7} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.12	2B	$1088$	$1536$	$53$	$1$	$4$	$2$	$3$	$18432$	$1.733118$	$82483294977/17$	$1.03131$	$5.97853$	$[0, 0, 0, -419339, 104519162]$	\(y^2=x^3-419339x+104519162\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.8, 16.48.0-16.j.1.8, 32.96.0-32.f.2.7, $\ldots$	$[ ]$
4624.d2	4624e2	4624.d	4624e	$4$	$4$	\( 2^{4} \cdot 17^{2} \)	\( 2^{12} \cdot 17^{8} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.5	2Cs	$544$	$1536$	$53$	$1$	$4$	$2$	$3$	$9216$	$1.386543$	$20346417/289$	$1.02963$	$4.99412$	$[0, 0, 0, -26299, 1621290]$	\(y^2=x^3-26299x+1621290\)	2.6.0.a.1, 4.24.0-4.a.1.2, 8.48.0-8.f.1.4, 16.96.0-16.c.2.3, 68.48.0-68.b.1.2, $\ldots$	$[ ]$
4624.d3	4624e1	4624.d	4624e	$4$	$4$	\( 2^{4} \cdot 17^{2} \)	\( 2^{12} \cdot 17^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.0.20	2B	$1088$	$1536$	$53$	$1$	$1$		$1$	$4608$	$1.039970$	$35937/17$	$1.02432$	$4.24298$	$[0, 0, 0, -3179, -29478]$	\(y^2=x^3-3179x-29478\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.6, 16.48.0-16.j.1.6, 32.96.0-32.f.2.8, $\ldots$	$[ ]$
4624.d4	4624e4	4624.d	4624e	$4$	$4$	\( 2^{4} \cdot 17^{2} \)	\( - 2^{12} \cdot 17^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.96.0.186	2B	$1088$	$1536$	$53$	$1$	$4$	$2$	$1$	$18432$	$1.733118$	$-35937/83521$	$1.18071$	$5.22631$	$[0, 0, 0, -3179, 4372570]$	\(y^2=x^3-3179x+4372570\)	2.3.0.a.1, 4.12.0.d.1, 8.48.0-8.t.1.4, 16.96.0-16.m.2.3, 68.24.0-4.d.1.1, $\ldots$	$[ ]$
4624.e1	4624b2	4624.e	4624b	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{10} \cdot 17^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.12.0.18	2B	$136$	$48$	$1$	$4.088136378$	$1$		$3$	$17408$	$1.626400$	$1098500$	$0.91788$	$5.49114$	$[0, -1, 0, -106448, 13392656]$	\(y^2=x^3-x^2-106448x+13392656\)	2.3.0.a.1, 4.6.0.d.1, 8.12.0.x.1, 34.6.0.a.1, 68.24.0-68.i.1.2, $\ldots$	$[(112, 1692)]$
4624.e2	4624b1	4624.e	4624b	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{8} \cdot 17^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.12.0.18	2B	$136$	$48$	$1$	$8.176272757$	$1$		$1$	$8704$	$1.279827$	$2000$	$0.77446$	$4.57933$	$[0, -1, 0, -8188, 107904]$	\(y^2=x^3-x^2-8188x+107904\)	2.3.0.a.1, 4.6.0.d.1, 8.12.0.x.1, 34.6.0.a.1, 68.24.0-68.i.1.1, $\ldots$	$[(1060/9, 38728/9)]$
4624.f1	4624a2	4624.f	4624a	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{11} \cdot 17^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$136$	$12$	$0$	$5.708120250$	$1$		$1$	$9216$	$1.284761$	$6097250/289$	$0.87700$	$4.76919$	$[0, -1, 0, -13968, -604192]$	\(y^2=x^3-x^2-13968x-604192\)	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[(-542/3, 3302/3)]$
4624.f2	4624a1	4624.f	4624a	$2$	$2$	\( 2^{4} \cdot 17^{2} \)	\( 2^{10} \cdot 17^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$136$	$12$	$0$	$2.854060125$	$1$		$3$	$4608$	$0.938188$	$62500/17$	$0.89869$	$4.14428$	$[0, -1, 0, -2408, 33920]$	\(y^2=x^3-x^2-2408x+33920\)	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[(4, 156)]$

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