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Results (40 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
150.1-a1 150.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.529028794$ 1.999098632 \( -\frac{112972667}{30000} a + \frac{282187521}{40000} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -5 a - 13\) , \( -15 a - 37\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a-13\right){x}-15a-37$
150.1-a2 150.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.632257198$ 1.999098632 \( -\frac{4778868950563904371}{1831054687500} a + \frac{1952082876040517781}{305175781250} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -75 a - 273\) , \( -519 a - 1641\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-75a-273\right){x}-519a-1641$
150.1-a3 150.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.264514397$ 1.999098632 \( \frac{2583922302027}{1562500} a + \frac{38016780418783}{9375000} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -85 a - 213\) , \( -711 a - 1749\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-85a-213\right){x}-711a-1749$
150.1-a4 150.1-a \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.816128599$ 1.999098632 \( \frac{33523849577935233}{2500} a + \frac{369523465565516147}{11250} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1375 a - 3353\) , \( -43847 a - 107425\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1375a-3353\right){x}-43847a-107425$
150.1-b1 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.335468070$ 3.286902394 \( -\frac{8889588234944170142939}{7031250} a + \frac{1209719733278025672168}{390625} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5606 a - 13776\) , \( -395577 a - 969132\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5606a-13776\right){x}-395577a-969132$
150.1-b2 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( -\frac{273359449}{1536000} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 271 a - 661\) , \( -12352 a + 30257\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(271a-661\right){x}-12352a+30257$
150.1-b3 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( \frac{357911}{2160} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -29 a + 74\) , \( 416 a - 1018\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-29a+74\right){x}+416a-1018$
150.1-b4 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.335468070$ 3.286902394 \( -\frac{26673883482189453500771}{715255737304687500} a + \frac{5545867307448315927528}{59604644775390625} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 35919 a + 87939\) , \( 803878 a + 1968921\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(35919a+87939\right){x}+803878a+1968921$
150.1-b5 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.341872283$ 3.286902394 \( \frac{10316097499609}{5859375000} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -9071 a - 22221\) , \( 98592 a + 241497\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-9071a-22221\right){x}+98592a+241497$
150.1-b6 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( \frac{35578826569}{5314410} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1371 a - 3356\) , \( -36992 a + 90612\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(1371a-3356\right){x}-36992a+90612$
150.1-b7 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( \frac{702595369}{72900} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -371 a - 906\) , \( -5568 a - 13638\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-371a-906\right){x}-5568a-13638$
150.1-b8 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.335468070$ 3.286902394 \( \frac{26673883482189453500771}{715255737304687500} a + \frac{5545867307448315927528}{59604644775390625} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -35919 a + 87939\) , \( -803878 a + 1968921\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-35919a+87939\right){x}-803878a+1968921$
150.1-b9 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( \frac{4102915888729}{9000000} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -6671 a - 16341\) , \( 462144 a + 1132017\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-6671a-16341\right){x}+462144a+1132017$
150.1-b10 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.341872283$ 3.286902394 \( \frac{2656166199049}{33750} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5771 a - 14136\) , \( -374496 a - 917328\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5771a-14136\right){x}-374496a-917328$
150.1-b11 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/12\Z$ $\mathrm{SU}(2)$ $1$ $5.367489134$ 3.286902394 \( \frac{16778985534208729}{81000} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -106671 a - 261341\) , \( 29666144 a + 72667017\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-106671a-261341\right){x}+29666144a+72667017$
150.1-b12 150.1-b \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.335468070$ 3.286902394 \( \frac{8889588234944170142939}{7031250} a + \frac{1209719733278025672168}{390625} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 5606 a - 13776\) , \( 395577 a - 969132\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(5606a-13776\right){x}+395577a-969132$
150.1-c1 150.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.816128599$ 1.999098632 \( -\frac{33523849577935233}{2500} a + \frac{369523465565516147}{11250} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 1374 a - 3353\) , \( 43846 a - 107425\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1374a-3353\right){x}+43846a-107425$
150.1-c2 150.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.264514397$ 1.999098632 \( -\frac{2583922302027}{1562500} a + \frac{38016780418783}{9375000} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 84 a - 213\) , \( 710 a - 1749\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(84a-213\right){x}+710a-1749$
150.1-c3 150.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.529028794$ 1.999098632 \( \frac{112972667}{30000} a + \frac{282187521}{40000} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 4 a - 13\) , \( 14 a - 37\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4a-13\right){x}+14a-37$
150.1-c4 150.1-c \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.632257198$ 1.999098632 \( \frac{4778868950563904371}{1831054687500} a + \frac{1952082876040517781}{305175781250} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 74 a - 273\) , \( 518 a - 1641\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(74a-273\right){x}+518a-1641$
150.1-d1 150.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $5.381534970$ 1.573990516 \( -\frac{33523849577935233}{2500} a + \frac{369523465565516147}{11250} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 291 a + 645\) , \( 5778 a + 14337\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(291a+645\right){x}+5778a+14337$
150.1-d2 150.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.089553297$ $10.76306994$ 1.573990516 \( -\frac{2583922302027}{1562500} a + \frac{38016780418783}{9375000} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -119 a - 295\) , \( 720 a + 1765\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-119a-295\right){x}+720a+1765$
150.1-d3 150.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $10.76306994$ 1.573990516 \( \frac{112972667}{30000} a + \frac{282187521}{40000} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -39 a - 95\) , \( -256 a - 627\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-39a-95\right){x}-256a-627$
150.1-d4 150.1-d \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $5.381534970$ 1.573990516 \( \frac{4778868950563904371}{1831054687500} a + \frac{1952082876040517781}{305175781250} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1809 a - 4435\) , \( 63246 a + 154921\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1809a-4435\right){x}+63246a+154921$
150.1-e1 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.508372848$ $5.617778566$ 1.917607978 \( -\frac{8889588234944170142939}{7031250} a + \frac{1209719733278025672168}{390625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 885 a - 2449\) , \( -24162 a + 61154\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(885a-2449\right){x}-24162a+61154$
150.1-e2 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.762559272$ $1.248395236$ 1.917607978 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$
150.1-e3 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.254186424$ $11.23555713$ 1.917607978 \( \frac{357911}{2160} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$
150.1-e4 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.525118545$ $0.624197618$ 1.917607978 \( -\frac{26673883482189453500771}{715255737304687500} a + \frac{5545867307448315927528}{59604644775390625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1310 a - 1414\) , \( -25288 a + 58064\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(1310a-1414\right){x}-25288a+58064$
150.1-e5 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.762559272$ $1.248395236$ 1.917607978 \( \frac{10316097499609}{5859375000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$
150.1-e6 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.254186424$ $2.808889283$ 1.917607978 \( \frac{35578826569}{5314410} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
150.1-e7 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $0.627093212$ $11.23555713$ 1.917607978 \( \frac{702595369}{72900} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$
150.1-e8 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.525118545$ $0.624197618$ 1.917607978 \( \frac{26673883482189453500771}{715255737304687500} a + \frac{5545867307448315927528}{59604644775390625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1310 a - 1414\) , \( 25288 a + 58064\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-1310a-1414\right){x}+25288a+58064$
150.1-e9 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.881279636$ $1.248395236$ 1.917607978 \( \frac{4102915888729}{9000000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
150.1-e10 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1.254186424$ $11.23555713$ 1.917607978 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
150.1-e11 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.762559272$ $0.312098809$ 1.917607978 \( \frac{16778985534208729}{81000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$
150.1-e12 150.1-e \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.508372848$ $5.617778566$ 1.917607978 \( \frac{8889588234944170142939}{7031250} a + \frac{1209719733278025672168}{390625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -885 a - 2449\) , \( 24162 a + 61154\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-885a-2449\right){x}+24162a+61154$
150.1-f1 150.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $10.76306994$ 1.573990516 \( -\frac{112972667}{30000} a + \frac{282187521}{40000} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 39 a - 95\) , \( 256 a - 627\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(39a-95\right){x}+256a-627$
150.1-f2 150.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $5.381534970$ 1.573990516 \( -\frac{4778868950563904371}{1831054687500} a + \frac{1952082876040517781}{305175781250} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1809 a - 4435\) , \( -63246 a + 154921\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1809a-4435\right){x}-63246a+154921$
150.1-f3 150.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.089553297$ $10.76306994$ 1.573990516 \( \frac{2583922302027}{1562500} a + \frac{38016780418783}{9375000} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 119 a - 295\) , \( -720 a + 1765\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(119a-295\right){x}-720a+1765$
150.1-f4 150.1-f \(\Q(\sqrt{6}) \) \( 2 \cdot 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.179106595$ $5.381534970$ 1.573990516 \( \frac{33523849577935233}{2500} a + \frac{369523465565516147}{11250} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -291 a + 645\) , \( -5778 a + 14337\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-291a+645\right){x}-5778a+14337$
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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.