Elliptic curves over Q(15)\Q(\sqrt{15})

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
8.1-a1	8.1-a	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{16}$	$1.16409$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$21.87465325$	1.536384471	$-432$	$\bigl[0$ , $a$ , $0$ , $-8 a - 26$ , $-64 a - 250\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-8a-26\right){x}-64a-250$
8.1-a2	8.1-a	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{22}$	$1.16409$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$21.87465325$	1.536384471	$-128955875202 a + 499443959016$	$\bigl[0$ , $a$ , $0$ , $-208 a - 806$ , $-1388 a - 5366\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-208a-806\right){x}-1388a-5366$
8.1-a3	8.1-a	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{20}$	$1.16409$	$(2,a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	$2^{2}$	$1.088088831$	$21.87465325$	1.536384471	$1000188$	$\bigl[0$ , $a$ , $0$ , $-168 a - 646$ , $-2548 a - 9870\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-168a-646\right){x}-2548a-9870$
8.1-a4	8.1-a	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{22}$	$1.16409$	$(2,a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$5.468663313$	1.536384471	$128955875202 a + 499443959016$	$\bigl[0$ , $a$ , $0$ , $-2688 a - 10406$ , $-152764 a - 591654\bigr]$	${y}^2={x}^{3}+a{x}^{2}+\left(-2688a-10406\right){x}-152764a-591654$
8.1-b1	8.1-b	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{4}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$1$	$21.87465325$	1.412002795	$-432$	$\bigl[a + 1$ , $-a - 1$ , $0$ , $-125 a - 476$ , $3263 a + 12642\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-125a-476\right){x}+3263a+12642$
8.1-b2	8.1-b	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{10}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$4$	$2$	$1$	$5.468663313$	1.412002795	$-128955875202 a + 499443959016$	$\bigl[a + 1$ , $-a - 1$ , $0$ , $-3235 a - 12521$ , $67026 a + 259595\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3235a-12521\right){x}+67026a+259595$
8.1-b3	8.1-b	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{8}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$4$	$2$	$1$	$21.87465325$	1.412002795	$1000188$	$\bigl[a + 1$ , $-a - 1$ , $0$ , $-2605 a - 10081$ , $141300 a + 547257\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2605a-10081\right){x}+141300a+547257$
8.1-b4	8.1-b	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{10}$	$1.16409$	$(2,a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$4$	$2$	$1$	$21.87465325$	1.412002795	$128955875202 a + 499443959016$	$\bigl[a + 1$ , $-a - 1$ , $0$ , $-41655 a - 161321$ , $9092142 a + 35213719\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-41655a-161321\right){x}+9092142a+35213719$
8.1-c1	8.1-c	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{16}$	$1.16409$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$21.87465325$	1.536384471	$-432$	$\bigl[0$ , $-a$ , $0$ , $-8 a - 26$ , $64 a + 250\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(-8a-26\right){x}+64a+250$
8.1-c2	8.1-c	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{22}$	$1.16409$	$(2,a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$5.468663313$	1.536384471	$-128955875202 a + 499443959016$	$\bigl[0$ , $-a$ , $0$ , $-208 a - 806$ , $1388 a + 5366\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(-208a-806\right){x}+1388a+5366$
8.1-c3	8.1-c	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{20}$	$1.16409$	$(2,a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$1$	$2^{2}$	$1.088088831$	$21.87465325$	1.536384471	$1000188$	$\bigl[0$ , $-a$ , $0$ , $-168 a - 646$ , $2548 a + 9870\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(-168a-646\right){x}+2548a+9870$
8.1-c4	8.1-c	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{22}$	$1.16409$	$(2,a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$2.176177662$	$21.87465325$	1.536384471	$128955875202 a + 499443959016$	$\bigl[0$ , $-a$ , $0$ , $-2688 a - 10406$ , $152764 a + 591654\bigr]$	${y}^2={x}^{3}-a{x}^{2}+\left(-2688a-10406\right){x}+152764a+591654$
8.1-d1	8.1-d	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{4}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$1$	$2$	$1$	$21.87465325$	1.412002795	$-432$	$\bigl[a + 1$ , $-1$ , $a + 1$ , $-4$ , $-2\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-4{x}-2$
8.1-d2	8.1-d	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{10}$	$1.16409$	$(2,a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$4$	$2$	$1$	$21.87465325$	1.412002795	$-128955875202 a + 499443959016$	$\bigl[a + 1$ , $-1$ , $a + 1$ , $10 a - 49$ , $-36 a + 125\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(10a-49\right){x}-36a+125$
8.1-d3	8.1-d	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{8}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2Cs	$4$	$2$	$1$	$21.87465325$	1.412002795	$1000188$	$\bigl[a + 1$ , $-1$ , $a + 1$ , $-9$ , $-2 a - 7\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-9{x}-2a-7$
8.1-d4	8.1-d	$4$	$4$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	8.1	$2^{3}$	$2^{10}$	$1.16409$	$(2,a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2$	2B	$4$	$2$	$1$	$5.468663313$	1.412002795	$128955875202 a + 499443959016$	$\bigl[a + 1$ , $-1$ , $a + 1$ , $-10 a - 49$ , $-56 a - 219\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-10a-49\right){x}-56a-219$
10.1-a1	10.1-a	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{2} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2}$	$1$	$22.35500709$	0.320668778	$-\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a$ , $-a + 1$ , $a$ , $-3 a + 4$ , $-2 a + 4\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+4\right){x}-2a+4$
10.1-a2	10.1-a	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{6} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$2.483889677$	0.320668778	$\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a$ , $-a + 1$ , $a$ , $27 a - 111$ , $260 a - 1010\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(27a-111\right){x}+260a-1010$
10.1-a3	10.1-a	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{3} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$4$	$1$	$1$	$2.483889677$	0.320668778	$-\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a$ , $-a + 1$ , $a$ , $477 a - 1861$ , $12680 a - 49110\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(477a-1861\right){x}+12680a-49110$
10.1-a4	10.1-a	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2 \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$4$	$1$	$1$	$22.35500709$	0.320668778	$\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a$ , $-a + 1$ , $a$ , $2 a - 21$ , $30 a - 116\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-21\right){x}+30a-116$
10.1-b1	10.1-b	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{6} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$-\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a$ , $a - 1$ , $a$ , $-402 a + 1564$ , $14377 a - 55675\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-402a+1564\right){x}+14377a-55675$
10.1-b2	10.1-b	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{2} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a$ , $a - 1$ , $a$ , $188 a - 721$ , $2661 a - 10299\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(188a-721\right){x}+2661a-10299$
10.1-b3	10.1-b	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2 \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$11.26497123$	1.454301533	$-\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a$ , $a - 1$ , $a$ , $2983 a - 11546$ , $173253 a - 670999\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2983a-11546\right){x}+173253a-670999$
10.1-b4	10.1-b	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{3} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$11.26497123$	1.454301533	$\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a$ , $a - 1$ , $a$ , $3148 a - 12186$ , $152797 a - 591775\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3148a-12186\right){x}+152797a-591775$
10.1-c1	10.1-c	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{18} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3^{2}$	$1$	$11.26497123$	1.454301533	$-\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a + 1$ , $a$ , $0$ , $-24 a + 110$ , $250 a - 960\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-24a+110\right){x}+250a-960$
10.1-c2	10.1-c	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{14} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a + 1$ , $a$ , $0$ , $16 a - 30$ , $42 a - 128\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(16a-30\right){x}+42a-128$
10.1-c3	10.1-c	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{13} \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$4$	$1$	$1$	$11.26497123$	1.454301533	$-\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a + 1$ , $a$ , $0$ , $196 a - 730$ , $2746 a - 10608\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(196a-730\right){x}+2746a-10608$
10.1-c4	10.1-c	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{15} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$4$	$3^{2}$	$1$	$11.26497123$	1.454301533	$\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a + 1$ , $a$ , $0$ , $176 a - 890$ , $2490 a - 8960\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(176a-890\right){x}+2490a-8960$
10.1-d1	10.1-d	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{14} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$22.35500709$	2.886019006	$-\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $54 a - 205$ , $1800 a - 6965\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(54a-205\right){x}+1800a-6965$
10.1-d2	10.1-d	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{18} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2} \cdot 3^{2}$	$1$	$2.483889677$	2.886019006	$\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $7454 a - 28865$ , $696920 a - 2699153\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(7454a-28865\right){x}+696920a-2699153$
10.1-d3	10.1-d	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{15} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$3^{2}$	$1$	$2.483889677$	2.886019006	$-\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $119254 a - 461865$ , $44237360 a - 171330553\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(119254a-461865\right){x}+44237360a-171330553$
10.1-d4	10.1-d	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{13} \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$22.35500709$	2.886019006	$\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $1474 a - 5705$ , $61924 a - 239825\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1474a-5705\right){x}+61924a-239825$
10.1-e1	10.1-e	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{14} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$-\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a + 1$ , $-a$ , $0$ , $52 a - 200$ , $-1640 a + 6352\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(52a-200\right){x}-1640a+6352$
10.1-e2	10.1-e	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{18} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3^{2}$	$1$	$11.26497123$	1.454301533	$\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a + 1$ , $-a$ , $0$ , $7452 a - 28860$ , $-674560 a + 2612560\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(7452a-28860\right){x}-674560a+2612560$
10.1-e3	10.1-e	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{15} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$4$	$3^{2}$	$1$	$11.26497123$	1.454301533	$-\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a + 1$ , $-a$ , $0$ , $119252 a - 461860$ , $-43879600 a + 169944960\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(119252a-461860\right){x}-43879600a+169944960$
10.1-e4	10.1-e	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{13} \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$4$	$1$	$1$	$11.26497123$	1.454301533	$\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a + 1$ , $-a$ , $0$ , $1472 a - 5700$ , $-57504 a + 222712\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(1472a-5700\right){x}-57504a+222712$
10.1-f1	10.1-f	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{18} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2} \cdot 3^{2}$	$1$	$2.483889677$	2.886019006	$-\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $-23 a + 113$ , $-230 a + 861\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a+113\right){x}-230a+861$
10.1-f2	10.1-f	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{14} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$22.35500709$	2.886019006	$\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $17 a - 27$ , $-42 a + 209\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a-27\right){x}-42a+209$
10.1-f3	10.1-f	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{13} \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$22.35500709$	2.886019006	$-\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $197 a - 727$ , $-2906 a + 11289\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(197a-727\right){x}-2906a+11289$
10.1-f4	10.1-f	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{15} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$3^{2}$	$1$	$2.483889677$	2.886019006	$\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $177 a - 887$ , $-2870 a + 8861\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(177a-887\right){x}-2870a+8861$
10.1-g1	10.1-g	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{6} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$2.483889677$	0.320668778	$-\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[1$ , $-a$ , $0$ , $-404 a + 1569$ , $-14780 a + 57241\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-404a+1569\right){x}-14780a+57241$
10.1-g2	10.1-g	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{2} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2}$	$1$	$22.35500709$	0.320668778	$\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[1$ , $-a$ , $0$ , $186 a - 716$ , $-2474 a + 9580\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(186a-716\right){x}-2474a+9580$
10.1-g3	10.1-g	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2 \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$4$	$1$	$1$	$22.35500709$	0.320668778	$-\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[1$ , $-a$ , $0$ , $2981 a - 11541$ , $-170271 a + 659455\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(2981a-11541\right){x}-170271a+659455$
10.1-g4	10.1-g	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{3} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$4$	$1$	$1$	$2.483889677$	0.320668778	$\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[1$ , $-a$ , $0$ , $3146 a - 12181$ , $-149650 a + 579591\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3146a-12181\right){x}-149650a+579591$
10.1-h1	10.1-h	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{2} \cdot 5^{2}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$-\frac{368271}{10} a - \frac{713678}{5}$	$\bigl[1$ , $a + 1$ , $1$ , $a + 4$ , $4\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$
10.1-h2	10.1-h	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{6} \cdot 5^{6}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$11.26497123$	1.454301533	$\frac{22896613727}{1000} a - \frac{22169433439}{250}$	$\bigl[1$ , $a + 1$ , $1$ , $31 a - 111$ , $-202 a + 788\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(31a-111\right){x}-202a+788$
10.1-h3	10.1-h	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2^{3} \cdot 5^{3}$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$11.26497123$	1.454301533	$-\frac{406087370211328559}{100} a + \frac{314553924386830927}{20}$	$\bigl[1$ , $a + 1$ , $1$ , $481 a - 1861$ , $-11722 a + 45388\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(481a-1861\right){x}-11722a+45388$
10.1-h4	10.1-h	$4$	$6$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$2 \cdot 5$	$1.23088$	$(2,a+1), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B	$4$	$1$	$1$	$11.26497123$	1.454301533	$\frac{105678766089}{10} a + \frac{81859053049}{2}$	$\bigl[1$ , $a + 1$ , $1$ , $6 a - 21$ , $-22 a + 74\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-21\right){x}-22a+74$
14.1-a1	14.1-a	$3$	$9$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$- 2^{3} \cdot 7$	$1.33889$	$(2,a+1), (7,a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$9$	$3$	$1$	$0.760182873$	2.649758048	$-\frac{632235090508565}{28} a - \frac{2448631469962925}{28}$	$\bigl[a$ , $1$ , $1$ , $5060 a - 19593$ , $393664 a - 1524653\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(5060a-19593\right){x}+393664a-1524653$
14.1-a2	14.1-a	$3$	$9$	$\Q(\sqrt{15})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$- 2^{9} \cdot 7^{3}$	$1.33889$	$(2,a+1), (7,a+1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Cs.1.1	$1$	$3^{3}$	$1$	$6.841645863$	2.649758048	$-\frac{80643645}{10976} a - \frac{293363275}{10976}$	$\bigl[a$ , $1$ , $1$ , $90 a - 343$ , $152 a - 585\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(90a-343\right){x}+152a-585$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.