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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
31.1-a1 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/8\Z$ $1$ $51.50883971$ 0.359928959 \( -\frac{106208}{31} a + \frac{51455}{31} \) \( \bigl[1\) , \( \phi + 1\) , \( \phi\) , \( \phi\) , \( 0\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\phi{x}$
31.1-a2 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $1.609651241$ 0.359928959 \( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) \( \bigl[\phi\) , \( -1\) , \( \phi + 1\) , \( 133 \phi - 141\) , \( 737 \phi - 764\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(133\phi-141\right){x}+737\phi-764$
31.1-a3 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.438604964$ 0.359928959 \( -\frac{156520379364360}{923521} a + \frac{253260256463213}{923521} \) \( \bigl[\phi\) , \( -1\) , \( \phi + 1\) , \( -12 \phi - 21\) , \( 42 \phi + 10\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(-12\phi-21\right){x}+42\phi+10$
31.1-a4 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $1.609651241$ 0.359928959 \( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) \( \bigl[1\) , \( \phi + 1\) , \( \phi\) , \( 31 \phi - 75\) , \( 141 \phi - 303\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(31\phi-75\right){x}+141\phi-303$
31.1-a5 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $25.75441985$ 0.359928959 \( \frac{9029272560}{961} a + \frac{5599830233}{961} \) \( \bigl[1\) , \( \phi + 1\) , \( \phi\) , \( \phi - 5\) , \( 3 \phi - 5\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-5\right){x}+3\phi-5$
31.1-a6 31.1-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/4\Z$ $1$ $12.87720992$ 0.359928959 \( \frac{6130703730739448}{31} a + \frac{3788983280553597}{31} \) \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( -18 \phi + 15\) , \( 171 \phi - 265\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-18\phi+15\right){x}+171\phi-265$
31.2-a1 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $1.609651241$ 0.359928959 \( -\frac{11889611722383394}{852891037441} a + \frac{3260226660263703}{852891037441} \) \( \bigl[1\) , \( -\phi - 1\) , \( \phi\) , \( -30 \phi - 45\) , \( -111 \phi - 117\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-30\phi-45\right){x}-111\phi-117$
31.2-a2 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/4\Z$ $1$ $12.87720992$ 0.359928959 \( -\frac{6130703730739448}{31} a + \frac{9919687011293045}{31} \) \( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( 16 \phi - 2\) , \( -172 \phi - 94\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(16\phi-2\right){x}-172\phi-94$
31.2-a3 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/8\Z$ $1$ $51.50883971$ 0.359928959 \( \frac{106208}{31} a - \frac{54753}{31} \) \( \bigl[1\) , \( -\phi - 1\) , \( \phi\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}$
31.2-a4 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $25.75441985$ 0.359928959 \( -\frac{9029272560}{961} a + \frac{14629102793}{961} \) \( \bigl[1\) , \( -\phi - 1\) , \( \phi\) , \( -5\) , \( -3 \phi + 3\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}-5{x}-3\phi+3$
31.2-a5 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $6.438604964$ 0.359928959 \( \frac{156520379364360}{923521} a + \frac{96739877098853}{923521} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi\) , \( 10 \phi - 32\) , \( -43 \phi + 53\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(10\phi-32\right){x}-43\phi+53$
31.2-a6 31.2-a \(\Q(\sqrt{5}) \) \( 31 \) $0$ $\Z/2\Z$ $1$ $1.609651241$ 0.359928959 \( \frac{61725871986044215714}{961} a + \frac{38148686872600722809}{961} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( \phi\) , \( -135 \phi - 7\) , \( -738 \phi - 26\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-135\phi-7\right){x}-738\phi-26$
36.1-a1 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $44.29962169$ 0.396227861 \( -\frac{24389}{12} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}$
36.1-a2 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $1.771984867$ 0.396227861 \( -\frac{19465109}{248832} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -5 \phi - 5\) , \( -51 \phi - 37\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}+\phi{x}^{2}+\left(-5\phi-5\right){x}-51\phi-37$
36.1-a3 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/2\Z$ $1$ $1.771984867$ 0.396227861 \( \frac{502270291349}{1889568} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 165 \phi - 331\) , \( 1352 \phi - 2408\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(165\phi-331\right){x}+1352\phi-2408$
36.1-a4 36.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \) $0$ $\Z/10\Z$ $1$ $44.29962169$ 0.396227861 \( \frac{131872229}{18} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 10 \phi - 21\) , \( -31 \phi + 51\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(10\phi-21\right){x}-31\phi+51$
41.1-a1 41.1-a \(\Q(\sqrt{5}) \) \( 41 \) $0$ $\Z/7\Z$ $1$ $46.26087846$ 0.422214159 \( -\frac{176128}{41} a - \frac{110592}{41} \) \( \bigl[0\) , \( -\phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \) ${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}$
41.1-a2 41.1-a \(\Q(\sqrt{5}) \) \( 41 \) $0$ $\mathsf{trivial}$ $1$ $0.944099560$ 0.422214159 \( \frac{7215644871110656}{194754273881} a - \frac{11892928131395584}{194754273881} \) \( \bigl[0\) , \( -\phi\) , \( \phi\) , \( 10 \phi - 40\) , \( 31 \phi - 113\bigr] \) ${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}+\left(10\phi-40\right){x}+31\phi-113$
41.2-a1 41.2-a \(\Q(\sqrt{5}) \) \( 41 \) $0$ $\mathsf{trivial}$ $1$ $0.944099560$ 0.422214159 \( -\frac{7215644871110656}{194754273881} a - \frac{4677283260284928}{194754273881} \) \( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( -10 \phi - 30\) , \( -32 \phi - 82\bigr] \) ${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-10\phi-30\right){x}-32\phi-82$
41.2-a2 41.2-a \(\Q(\sqrt{5}) \) \( 41 \) $0$ $\Z/7\Z$ $1$ $46.26087846$ 0.422214159 \( \frac{176128}{41} a - \frac{286720}{41} \) \( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( 0\) , \( -\phi\bigr] \) ${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}-\phi$
45.1-a1 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $0.122605555$ 0.438646969 \( -\frac{152409672113485069453847362}{45} a + \frac{246604029693845863366701161}{45} \) \( \bigl[\phi\) , \( \phi + 1\) , \( 1\) , \( -4364 \phi - 7739\) , \( -255406 \phi - 296465\bigr] \) ${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(-4364\phi-7739\right){x}-255406\phi-296465$
45.1-a2 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/4\Z$ $1$ $0.490422220$ 0.438646969 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
45.1-a3 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $31.38702211$ 0.438646969 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
45.1-a4 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $1.961688882$ 0.438646969 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
45.1-a5 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $7.846755528$ 0.438646969 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
45.1-a6 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $31.38702211$ 0.438646969 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
45.1-a7 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $1.961688882$ 0.438646969 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
45.1-a8 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $31.38702211$ 0.438646969 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
45.1-a9 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.490422220$ 0.438646969 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
45.1-a10 45.1-a \(\Q(\sqrt{5}) \) \( 3^{2} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $0.122605555$ 0.438646969 \( \frac{152409672113485069453847362}{45} a + \frac{94194357580360793912853799}{45} \) \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( 4364 \phi - 12105\) , \( 243301 \phi - 535402\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(4364\phi-12105\right){x}+243301\phi-535402$
49.1-a1 49.1-a \(\Q(\sqrt{5}) \) \( 7^{2} \) $0$ $\mathsf{trivial}$ $1$ $1.045448192$ 0.467538645 \( -\frac{2887553024}{16807} \) \( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -30 \phi - 29\) , \( -102 \phi - 84\bigr] \) ${y}^2+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-30\phi-29\right){x}-102\phi-84$
49.1-a2 49.1-a \(\Q(\sqrt{5}) \) \( 7^{2} \) $0$ $\Z/5\Z$ $1$ $26.13620482$ 0.467538645 \( \frac{4096}{7} \) \( \bigl[0\) , \( \phi\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+\phi{x}^{2}+{x}$
55.1-a1 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $19.86707574$ 0.493601465 \( -\frac{626283905886387}{73205} a + \frac{1013348626965991}{73205} \) \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( 9 \phi - 25\) , \( -6 \phi + 44\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(9\phi-25\right){x}-6\phi+44$
55.1-a2 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $2.207452860$ 0.493601465 \( -\frac{114278307303626907}{78460709418025} a + \frac{203603378036088236}{78460709418025} \) \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( 54 \phi\) , \( -374 \phi - 198\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+54\phi{x}-374\phi-198$
55.1-a3 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $39.73415148$ 0.493601465 \( \frac{45227}{55} a + \frac{26979}{55} \) \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -\phi - 1\) , \( -\phi\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-\phi-1\right){x}-\phi$
55.1-a4 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.414905721$ 0.493601465 \( -\frac{1485675267531}{221445125} a + \frac{4152064659709}{221445125} \) \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( -21 \phi - 25\) , \( -54 \phi - 58\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-21\phi-25\right){x}-54\phi-58$
55.1-a5 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $2.207452860$ 0.493601465 \( -\frac{4560282420936767}{20796875} a + \frac{7378860561741612}{20796875} \) \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( -16 \phi - 210\) , \( 1110 \phi - 534\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-16\phi-210\right){x}+1110\phi-534$
55.1-a6 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $39.73415148$ 0.493601465 \( \frac{132583563}{605} a + \frac{166070482}{605} \) \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( 4 \phi - 11\) , \( -9 \phi + 13\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(4\phi-11\right){x}-9\phi+13$
55.1-a7 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $4.414905721$ 0.493601465 \( \frac{754904381777}{33275} a + \frac{466557150454}{33275} \) \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -6 \phi - 1\) , \( \phi - 17\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-6\phi-1\right){x}+\phi-17$
55.1-a8 55.1-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $19.86707574$ 0.493601465 \( \frac{48555143354501}{275} a + \frac{30008729421823}{275} \) \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -6 \phi - 26\) , \( 28 \phi + 8\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-6\phi-26\right){x}+28\phi+8$
55.2-a1 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $39.73415148$ 0.493601465 \( -\frac{45227}{55} a + \frac{72206}{55} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -\phi\) , \( 0\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}-\phi{x}$
55.2-a2 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $4.414905721$ 0.493601465 \( -\frac{754904381777}{33275} a + \frac{1221461532231}{33275} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 5\) , \( -2 \phi - 15\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-5\right){x}-2\phi-15$
55.2-a3 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $19.86707574$ 0.493601465 \( -\frac{48555143354501}{275} a + \frac{78563872776324}{275} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 30\) , \( -29 \phi + 37\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(4\phi-30\right){x}-29\phi+37$
55.2-a4 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $2.207452860$ 0.493601465 \( \frac{114278307303626907}{78460709418025} a + \frac{89325070732461329}{78460709418025} \) \( \bigl[1\) , \( \phi\) , \( 1\) , \( -54 \phi + 54\) , \( 374 \phi - 572\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(-54\phi+54\right){x}+374\phi-572$
55.2-a5 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.414905721$ 0.493601465 \( \frac{1485675267531}{221445125} a + \frac{2666389392178}{221445125} \) \( \bigl[1\) , \( \phi\) , \( 1\) , \( 21 \phi - 46\) , \( 54 \phi - 112\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(21\phi-46\right){x}+54\phi-112$
55.2-a6 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ $1$ $39.73415148$ 0.493601465 \( -\frac{132583563}{605} a + \frac{59730809}{121} \) \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -6 \phi - 5\) , \( 8 \phi + 5\bigr] \) ${y}^2+\phi{x}{y}+\phi{y}={x}^{3}+\left(-\phi+1\right){x}^{2}+\left(-6\phi-5\right){x}+8\phi+5$
55.2-a7 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $2.207452860$ 0.493601465 \( \frac{4560282420936767}{20796875} a + \frac{563715628160969}{4159375} \) \( \bigl[1\) , \( \phi\) , \( 1\) , \( 16 \phi - 226\) , \( -1110 \phi + 576\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(16\phi-226\right){x}-1110\phi+576$
55.2-a8 55.2-a \(\Q(\sqrt{5}) \) \( 5 \cdot 11 \) $0$ $\Z/6\Z$ $1$ $19.86707574$ 0.493601465 \( \frac{626283905886387}{73205} a + \frac{387064721079604}{73205} \) \( \bigl[1\) , \( \phi\) , \( 1\) , \( -9 \phi - 16\) , \( 6 \phi + 38\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\phi{x}^{2}+\left(-9\phi-16\right){x}+6\phi+38$
64.1-a1 64.1-a \(\Q(\sqrt{5}) \) \( 2^{6} \) $0$ $\Z/2\Z$ $1$ $2.397417474$ 0.536078844 \( -2711191688 a + 4386800300 \) \( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 14 \phi - 25\) , \( \phi - 59\bigr] \) ${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+\left(14\phi-25\right){x}+\phi-59$
64.1-a2 64.1-a \(\Q(\sqrt{5}) \) \( 2^{6} \) $0$ $\Z/8\Z$ $1$ $19.17933979$ 0.536078844 \( -548896 a + 889584 \) \( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 4 \phi\) , \( 4\bigr] \) ${y}^2={x}^{3}+\left(\phi-1\right){x}^{2}+4\phi{x}+4$
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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.