Learn more

Refine search


Results (1-50 of 80 matches)

Next   Download to        
Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
320.1-a1 320.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.118391872$ $468.6067209$ 2.481106471 \( \frac{16364512939376012}{5} a^{3} - 3847527746699012 a^{2} - 11841472804798280 a + 13920486160220592 \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} - 2 a + 1\) , \( 16 a^{3} + 12 a^{2} - 73 a - 74\) , \( -82 a^{3} - 110 a^{2} + 256 a + 319\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(16a^{3}+12a^{2}-73a-74\right){x}-82a^{3}-110a^{2}+256a+319$
320.1-a2 320.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.059195936$ $1874.426883$ 2.481106471 \( \frac{124026912}{5} a^{3} - \frac{145264624}{5} a^{2} - 90071072 a + 105738976 \) \( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( a^{3} - 2 a + 1\) , \( a^{3} - 3 a^{2} - 8 a + 1\) , \( 9 a^{3} + 11 a^{2} - 30 a - 36\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(a^{3}-3a^{2}-8a+1\right){x}+9a^{3}+11a^{2}-30a-36$
320.1-a3 320.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.118391872$ $468.6067209$ 2.481106471 \( -\frac{904809174412}{5} a^{3} + 344228361732 a^{2} + 250084565320 a - 475710167264 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -24 a^{3} + 31 a^{2} + 95 a - 128\) , \( 99 a^{3} - 95 a^{2} - 391 a + 405\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(-24a^{3}+31a^{2}+95a-128\right){x}+99a^{3}-95a^{2}-391a+405$
320.1-a4 320.1-a \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.029597968$ $468.6067209$ 2.481106471 \( -\frac{10752}{5} a^{3} + \frac{10496}{5} a^{2} + \frac{39936}{5} a - \frac{38656}{5} \) \( \bigl[0\) , \( a^{2} - a - 3\) , \( 0\) , \( -2 a^{3} - 3 a^{2} + 8 a + 10\) , \( 3 a^{3} + 5 a^{2} - 12 a - 16\bigr] \) ${y}^2={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-2a^{3}-3a^{2}+8a+10\right){x}+3a^{3}+5a^{2}-12a-16$
320.1-b1 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $168.1973994$ 1.880504094 \( \frac{9285883494578}{5} a^{2} - \frac{12832775369604}{5} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 2 a + 1\) , \( -135 a^{3} - 282 a^{2} + 571 a + 845\) , \( -2158 a^{3} - 1611 a^{2} + 7136 a + 7109\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-135a^{3}-282a^{2}+571a+845\right){x}-2158a^{3}-1611a^{2}+7136a+7109$
320.1-b2 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $672.7895978$ 1.880504094 \( \frac{22755876}{25} a^{2} - \frac{31367044}{25} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 2 a + 1\) , \( 65 a^{3} + 68 a^{2} - 229 a - 255\) , \( -348 a^{3} - 391 a^{2} + 1246 a + 1439\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(65a^{3}+68a^{2}-229a-255\right){x}-348a^{3}-391a^{2}+1246a+1439$
320.1-b3 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/4\Z$ $1$ $168.1973994$ 1.880504094 \( \frac{2816}{5} a^{2} - 768 \) \( \bigl[0\) , \( -a^{2} + 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a^{2}+3\right){x}^{2}+{x}$
320.1-b4 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $42.04934986$ 1.880504094 \( -\frac{1444495316}{5} a^{2} + 1045299956 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( 0\) , \( -93 a^{3} - 177 a^{2} + 117 a + 230\) , \( -1108 a^{3} - 2113 a^{2} + 1510 a + 2895\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(-93a^{3}-177a^{2}+117a+230\right){x}-1108a^{3}-2113a^{2}+1510a+2895$
320.1-b5 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $672.7895978$ 1.880504094 \( -\frac{53328}{5} a^{2} + \frac{204544}{5} \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + a^{2} + 2 a - 3\) , \( 0\) , \( -13 a^{3} - 22 a^{2} + 17 a + 30\) , \( 18 a^{3} + 36 a^{2} - 25 a - 50\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-3\right){x}^{2}+\left(-13a^{3}-22a^{2}+17a+30\right){x}+18a^{3}+36a^{2}-25a-50$
320.1-b6 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $2.628084366$ 1.880504094 \( -\frac{396953189758099226}{5} a^{3} - 93329291315898880 a^{2} + 287238025770812558 a + 337668549509100264 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -45 a^{3} + 49 a^{2} + 185 a - 214\) , \( -442 a^{3} + 197 a^{2} + 1506 a - 1325\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-45a^{3}+49a^{2}+185a-214\right){x}-442a^{3}+197a^{2}+1506a-1325$
320.1-b7 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $168.1973994$ 1.880504094 \( -\frac{1613607658}{625} a^{2} + \frac{5837580356}{625} \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -145 a^{3} + 129 a^{2} + 495 a - 524\) , \( 1362 a^{3} - 1337 a^{2} - 4738 a + 5205\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-145a^{3}+129a^{2}+495a-524\right){x}+1362a^{3}-1337a^{2}-4738a+5205$
320.1-b8 320.1-b \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $2.628084366$ 1.880504094 \( \frac{396953189758099226}{5} a^{3} - 93329291315898880 a^{2} - 287238025770812558 a + 337668549509100264 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( 0\) , \( 45 a^{3} + 49 a^{2} - 185 a - 214\) , \( 442 a^{3} + 197 a^{2} - 1506 a - 1325\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-2\right){x}^{2}+\left(45a^{3}+49a^{2}-185a-214\right){x}+442a^{3}+197a^{2}-1506a-1325$
320.1-c1 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.381626126$ $81.99607002$ 2.798827484 \( \frac{22755876}{25} a^{2} - \frac{31367044}{25} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 4 a + 4\) , \( a^{2} + a - 3\) , \( 67 a^{3} + 64 a^{2} - 238 a - 244\) , \( 294 a^{3} + 322 a^{2} - 1052 a - 1190\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+4\right){x}^{2}+\left(67a^{3}+64a^{2}-238a-244\right){x}+294a^{3}+322a^{2}-1052a-1190$
320.1-c2 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.763252252$ $5.124754376$ 2.798827484 \( \frac{9285883494578}{5} a^{2} - \frac{12832775369604}{5} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 4 a + 4\) , \( a^{2} + a - 3\) , \( -133 a^{3} - 286 a^{2} + 562 a + 856\) , \( 2304 a^{3} + 1792 a^{2} - 7692 a - 7760\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+4\right){x}^{2}+\left(-133a^{3}-286a^{2}+562a+856\right){x}+2304a^{3}+1792a^{2}-7692a-7760$
320.1-c3 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.381626126$ $327.9842801$ 2.798827484 \( \frac{2816}{5} a^{2} - 768 \) \( \bigl[0\) , \( a^{2} - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a^{2}-3\right){x}^{2}+{x}$
320.1-c4 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.190813063$ $1311.937120$ 2.798827484 \( -\frac{53328}{5} a^{2} + \frac{204544}{5} \) \( \bigl[a^{3} - 2 a + 1\) , \( -1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -13 a^{3} - 24 a^{2} + 18 a + 32\) , \( -39 a^{3} - 74 a^{2} + 54 a + 102\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}-{x}^{2}+\left(-13a^{3}-24a^{2}+18a+32\right){x}-39a^{3}-74a^{2}+54a+102$
320.1-c5 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.381626126$ $1311.937120$ 2.798827484 \( -\frac{1444495316}{5} a^{2} + 1045299956 \) \( \bigl[a^{3} - 2 a + 1\) , \( -1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -93 a^{3} - 179 a^{2} + 118 a + 232\) , \( 947 a^{3} + 1810 a^{2} - 1281 a - 2468\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}-{x}^{2}+\left(-93a^{3}-179a^{2}+118a+232\right){x}+947a^{3}+1810a^{2}-1281a-2468$
320.1-c6 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.763252252$ $5.124754376$ 2.798827484 \( -\frac{1613607658}{625} a^{2} + \frac{5837580356}{625} \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 3\) , \( -145 a^{3} + 126 a^{2} + 495 a - 518\) , \( -1447 a^{3} + 1324 a^{2} + 4969 a - 5320\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-145a^{3}+126a^{2}+495a-518\right){x}-1447a^{3}+1324a^{2}+4969a-5320$
320.1-c7 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.763252252$ $327.9842801$ 2.798827484 \( \frac{396953189758099226}{5} a^{3} - 93329291315898880 a^{2} - 287238025770812558 a + 337668549509100264 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( 45 a^{3} + 46 a^{2} - 187 a - 208\) , \( -448 a^{3} - 220 a^{2} + 1468 a + 1300\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(45a^{3}+46a^{2}-187a-208\right){x}-448a^{3}-220a^{2}+1468a+1300$
320.1-c8 320.1-c \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.763252252$ $327.9842801$ 2.798827484 \( -\frac{396953189758099226}{5} a^{3} - 93329291315898880 a^{2} + 287238025770812558 a + 337668549509100264 \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 3\) , \( -45 a^{3} + 46 a^{2} + 185 a - 208\) , \( 447 a^{3} - 220 a^{2} - 1465 a + 1300\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-45a^{3}+46a^{2}+185a-208\right){x}+447a^{3}-220a^{2}-1465a+1300$
320.1-d1 320.1-d \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( \frac{16364512939376012}{5} a^{3} - 3847527746699012 a^{2} - 11841472804798280 a + 13920486160220592 \) \( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 17 a^{3} + 15 a^{2} - 76 a - 83\) , \( 98 a^{3} + 124 a^{2} - 329 a - 401\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(17a^{3}+15a^{2}-76a-83\right){x}+98a^{3}+124a^{2}-329a-401$
320.1-d2 320.1-d \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $240.7412310$ 1.345784394 \( \frac{124026912}{5} a^{3} - \frac{145264624}{5} a^{2} - 90071072 a + 105738976 \) \( \bigl[a^{2} + a - 3\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 2 a^{3} - 11 a - 8\) , \( -8 a^{3} - 12 a^{2} + 22 a + 29\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(2a^{3}-11a-8\right){x}-8a^{3}-12a^{2}+22a+29$
320.1-d3 320.1-d \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( -\frac{904809174412}{5} a^{3} + 344228361732 a^{2} + 250084565320 a - 475710167264 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a + 1\) , \( -25 a^{3} + 28 a^{2} + 99 a - 120\) , \( -94 a^{3} + 99 a^{2} + 363 a - 409\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-25a^{3}+28a^{2}+99a-120\right){x}-94a^{3}+99a^{2}+363a-409$
320.1-d4 320.1-d \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( -\frac{10752}{5} a^{3} + \frac{10496}{5} a^{2} + \frac{39936}{5} a - \frac{38656}{5} \) \( \bigl[0\) , \( -a^{2} + a + 3\) , \( 0\) , \( -2 a^{3} - 3 a^{2} + 8 a + 10\) , \( -3 a^{3} - 5 a^{2} + 12 a + 16\bigr] \) ${y}^2={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-2a^{3}-3a^{2}+8a+10\right){x}-3a^{3}-5a^{2}+12a+16$
320.1-e1 320.1-e \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( -\frac{1464004696636}{5} a^{3} - 344228361732 a^{2} + 1059364652864 a + 1245431641396 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 2 a + 3\) , \( a^{3} - 2 a + 1\) , \( 25 a^{3} - 31 a^{2} - 52 a + 28\) , \( 81 a^{3} - 101 a^{2} - 150 a + 91\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+3\right){x}^{2}+\left(25a^{3}-31a^{2}-52a+28\right){x}+81a^{3}-101a^{2}-150a+91$
320.1-e2 320.1-e \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $240.7412310$ 1.345784394 \( -\frac{78274624}{5} a^{3} + \frac{145264624}{5} a^{2} + 22159392 a - 39525648 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 2\) , \( a^{2} + a - 3\) , \( -4 a^{3} - 2 a^{2} + 9 a - 3\) , \( -2 a^{3} + 12 a^{2} + 14 a - 31\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-4a^{3}-2a^{2}+9a-3\right){x}-2a^{3}+12a^{2}+14a-31$
320.1-e3 320.1-e \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( -\frac{10113825205863364}{5} a^{3} + 3847527746699012 a^{2} + 2795392535642816 a - 5317152573274468 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} - a + 2\) , \( a^{2} + a - 3\) , \( -24 a^{3} - 17 a^{2} + 54 a - 3\) , \( -35 a^{3} - 124 a^{2} + 7 a + 219\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-24a^{3}-17a^{2}+54a-3\right){x}-35a^{3}-124a^{2}+7a+219$
320.1-e4 320.1-e \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( 1536 a^{3} - \frac{10496}{5} a^{2} - \frac{12288}{5} a + \frac{13824}{5} \) \( \bigl[0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 0\) , \( 2 a^{3} + 3 a^{2} - 4 a - 5\) , \( 3 a^{3} + 5 a^{2} - 6 a - 9\bigr] \) ${y}^2={x}^{3}+\left(a^{3}+a^{2}-3a-2\right){x}^{2}+\left(2a^{3}+3a^{2}-4a-5\right){x}+3a^{3}+5a^{2}-6a-9$
320.1-f1 320.1-f \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.118391872$ $468.6067209$ 2.481106471 \( \frac{1464004696636}{5} a^{3} - 344228361732 a^{2} - 1059364652864 a + 1245431641396 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -22 a^{3} - 28 a^{2} + 43 a + 21\) , \( 58 a^{3} + 72 a^{2} - 104 a - 70\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(-22a^{3}-28a^{2}+43a+21\right){x}+58a^{3}+72a^{2}-104a-70$
320.1-f2 320.1-f \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.118391872$ $468.6067209$ 2.481106471 \( \frac{10113825205863364}{5} a^{3} + 3847527746699012 a^{2} - 2795392535642816 a - 5317152573274468 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 24 a^{3} - 17 a^{2} - 56 a - 3\) , \( -35 a^{3} + 124 a^{2} + 7 a - 221\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(24a^{3}-17a^{2}-56a-3\right){x}-35a^{3}+124a^{2}+7a-221$
320.1-f3 320.1-f \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.059195936$ $1874.426883$ 2.481106471 \( \frac{78274624}{5} a^{3} + \frac{145264624}{5} a^{2} - 22159392 a - 39525648 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( 4 a^{3} - 2 a^{2} - 11 a - 3\) , \( -2 a^{3} - 12 a^{2} + 14 a + 29\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(4a^{3}-2a^{2}-11a-3\right){x}-2a^{3}-12a^{2}+14a+29$
320.1-f4 320.1-f \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.029597968$ $468.6067209$ 2.481106471 \( -1536 a^{3} - \frac{10496}{5} a^{2} + \frac{12288}{5} a + \frac{13824}{5} \) \( \bigl[0\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( -2 a^{3} + 3 a^{2} + 4 a - 5\) , \( 3 a^{3} - 5 a^{2} - 6 a + 9\bigr] \) ${y}^2={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-2a^{3}+3a^{2}+4a-5\right){x}+3a^{3}-5a^{2}-6a+9$
320.1-g1 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $310.7408534$ 1.737094179 \( \frac{148176}{25} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 2 a + 1\) , \( -21 a^{3} - 43 a^{2} + 27 a + 62\) , \( -107 a^{3} - 204 a^{2} + 148 a + 282\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-21a^{3}-43a^{2}+27a+62\right){x}-107a^{3}-204a^{2}+148a+282$
320.1-g2 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.213831458$ 1.737094179 \( -\frac{1565563717889316}{5} a^{2} + 1132852548571002 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 2 a + 1\) , \( -201 a^{3} - 448 a^{2} + 27 a + 287\) , \( -6493 a^{3} - 13023 a^{2} + 6703 a + 15182\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-201a^{3}-448a^{2}+27a+287\right){x}-6493a^{3}-13023a^{2}+6703a+15182$
320.1-g3 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $19.42130333$ 1.737094179 \( \frac{132304644}{5} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 0\) , \( 321 a^{3} - 616 a^{2} - 428 a + 833\) , \( 6456 a^{3} - 12299 a^{2} - 8866 a + 16931\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(321a^{3}-616a^{2}-428a+833\right){x}+6456a^{3}-12299a^{2}-8866a+16931$
320.1-g4 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/4\Z$ $1$ $19.42130333$ 1.737094179 \( \frac{237276}{625} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 0\) , \( -39 a^{3} + 74 a^{2} + 52 a - 97\) , \( 556 a^{3} - 1057 a^{2} - 768 a + 1459\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-39a^{3}+74a^{2}+52a-97\right){x}+556a^{3}-1057a^{2}-768a+1459$
320.1-g5 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.213831458$ 1.737094179 \( \frac{1565563717889316}{5} a^{2} - 432711169318314 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( a^{3} - 2 a + 1\) , \( 574 a^{3} + 445 a^{2} - 1924 a - 1946\) , \( 12775 a^{3} + 13021 a^{2} - 44818 a - 49928\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(574a^{3}+445a^{2}-1924a-1946\right){x}+12775a^{3}+13021a^{2}-44818a-49928$
320.1-g6 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $1242.963413$ 1.737094179 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \) ${y}^2={x}^{3}-2{x}+1$
320.1-g7 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $1242.963413$ 1.737094179 \( -\frac{237035808}{5} a^{2} + 171520848 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 4\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 11 a^{3} + 18 a^{2} - 21 a - 28\) , \( 92 a^{3} + 175 a^{2} - 125 a - 238\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+4\right){x}^{2}+\left(11a^{3}+18a^{2}-21a-28\right){x}+92a^{3}+175a^{2}-125a-238$
320.1-g8 320.1-g \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/8\Z$ $1$ $1242.963413$ 1.737094179 \( \frac{237035808}{5} a^{2} - 65514960 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 4\) , \( a^{3} - 2 a + 1\) , \( -8 a^{3} - 15 a^{2} + 35 a + 53\) , \( -127 a^{3} - 142 a^{2} + 457 a + 529\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+4\right){x}^{2}+\left(-8a^{3}-15a^{2}+35a+53\right){x}-127a^{3}-142a^{2}+457a+529$
320.1-h1 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.466696751$ $265.8178999$ 2.773984325 \( -\frac{1565563717889316}{5} a^{2} + 1132852548571002 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 0\) , \( -201 a^{3} - 446 a^{2} + 28 a + 283\) , \( 5882 a^{3} + 12073 a^{2} - 5316 a - 13311\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-201a^{3}-446a^{2}+28a+283\right){x}+5882a^{3}+12073a^{2}-5316a-13311$
320.1-h2 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.233348375$ $1063.271599$ 2.773984325 \( \frac{132304644}{5} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 2 a + 1\) , \( 321 a^{3} - 618 a^{2} - 429 a + 837\) , \( -6857 a^{3} + 13047 a^{2} + 9453 a - 18000\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(321a^{3}-618a^{2}-429a+837\right){x}-6857a^{3}+13047a^{2}+9453a-18000$
320.1-h3 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.233348375$ $66.45447499$ 2.773984325 \( \frac{237276}{625} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 0\) , \( 39 a^{3} + 74 a^{2} - 52 a - 97\) , \( 556 a^{3} + 1057 a^{2} - 768 a - 1459\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(39a^{3}+74a^{2}-52a-97\right){x}+556a^{3}+1057a^{2}-768a-1459$
320.1-h4 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.116674187$ $1063.271599$ 2.773984325 \( \frac{148176}{25} \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 7 a^{3} - 22 a - 10\) , \( -17 a^{3} - 8 a^{2} + 52 a + 45\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(7a^{3}-22a-10\right){x}-17a^{3}-8a^{2}+52a+45$
320.1-h5 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/4\Z$ $0.466696751$ $265.8178999$ 2.773984325 \( \frac{1565563717889316}{5} a^{2} - 432711169318314 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a - 1\) , \( 0\) , \( 575 a^{3} + 446 a^{2} - 1926 a - 1947\) , \( -12330 a^{3} - 12073 a^{2} + 42872 a + 47054\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(575a^{3}+446a^{2}-1926a-1947\right){x}-12330a^{3}-12073a^{2}+42872a+47054$
320.1-h6 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.233348375$ $265.8178999$ 2.773984325 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \) ${y}^2={x}^{3}-2{x}-1$
320.1-h7 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.466696751$ $66.45447499$ 2.773984325 \( -\frac{237035808}{5} a^{2} + 171520848 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 4\) , \( a^{2} + a - 3\) , \( 12 a^{3} + 17 a^{2} - 24 a - 25\) , \( -50 a^{3} - 98 a^{2} + 60 a + 124\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+4\right){x}^{2}+\left(12a^{3}+17a^{2}-24a-25\right){x}-50a^{3}-98a^{2}+60a+124$
320.1-h8 320.1-h \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $1$ $\Z/2\Z$ $0.466696751$ $66.45447499$ 2.773984325 \( \frac{237035808}{5} a^{2} - 65514960 \) \( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 4\) , \( 0\) , \( -7 a^{3} - 13 a^{2} + 33 a + 51\) , \( 115 a^{3} + 132 a^{2} - 410 a - 475\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-2a+4\right){x}^{2}+\left(-7a^{3}-13a^{2}+33a+51\right){x}+115a^{3}+132a^{2}-410a-475$
320.1-i1 320.1-i \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( \frac{1464004696636}{5} a^{3} - 344228361732 a^{2} - 1059364652864 a + 1245431641396 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 0\) , \( -21 a^{3} - 33 a^{2} + 37 a + 34\) , \( -116 a^{3} - 127 a^{2} + 224 a + 100\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(-21a^{3}-33a^{2}+37a+34\right){x}-116a^{3}-127a^{2}+224a+100$
320.1-i2 320.1-i \(\Q(\zeta_{20})^+\) \( 2^{6} \cdot 5 \) $0$ $\Z/2\Z$ $1$ $60.18530777$ 1.345784394 \( \frac{10113825205863364}{5} a^{3} + 3847527746699012 a^{2} - 2795392535642816 a - 5317152573274468 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( 24 a^{3} - 17 a^{2} - 56 a - 3\) , \( 34 a^{3} - 124 a^{2} - 4 a + 219\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(24a^{3}-17a^{2}-56a-3\right){x}+34a^{3}-124a^{2}-4a+219$
Next   Download to        

  *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.