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Results (21 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
900.1-a1 900.1-a \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.096436813$ 4.477355893 \( \frac{657300262000123}{37150418534400} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 12680 a + 39857\) , \( -14564747 a - 45734865\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(12680a+39857\right){x}-14564747a-45734865$
900.1-b1 900.1-b \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.094856309$ 3.765530159 \( \frac{97802241300184795037}{53747712000000000} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -671902 a - 2111688\) , \( 127257712 a + 399601092\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-671902a-2111688\right){x}+127257712a+399601092$
900.1-b2 900.1-b \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.023714077$ 3.765530159 \( \frac{87649400407713844299677}{632812500000000000} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -6477982 a - 20359368\) , \( -17036841872 a - 53497575996\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-6477982a-20359368\right){x}-17036841872a-53497575996$
900.1-c1 900.1-c \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.879573008$ 1.032716833 \( -\frac{30261551896446437}{150} a + \frac{375853462684920157}{450} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 674 a - 2776\) , \( 17951 a - 74315\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(674a-2776\right){x}+17951a-74315$
900.1-c2 900.1-c \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.518292035$ 1.032716833 \( -\frac{2801426243}{540} a + \frac{17847958663}{810} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 44 a - 166\) , \( 275 a - 1127\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(44a-166\right){x}+275a-1127$
900.1-d1 900.1-d \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.08846273$ 2.072559750 \( \frac{79507}{300} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 9 a + 30\) , \( 59 a + 185\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(9a+30\right){x}+59a+185$
900.1-d2 900.1-d \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.08846273$ 2.072559750 \( \frac{83453453}{11250} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -61 a - 190\) , \( 287 a + 901\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-61a-190\right){x}+287a+901$
900.1-e1 900.1-e \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.976308653$ 1.092375998 \( \frac{2712805671127662691}{777600} a - \frac{11231164533693007217}{777600} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -510 a - 1899\) , \( 17937 a + 58401\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-510a-1899\right){x}+17937a+58401$
900.1-f1 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.544707650$ $1.248395236$ 4.767964034 \( -\frac{273359449}{1536000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-14{x}-64$
900.1-f2 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $4.634122951$ $11.23555713$ 4.767964034 \( \frac{357911}{2160} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}+2$
900.1-f3 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.544707650$ $1.248395236$ 4.767964034 \( \frac{10316097499609}{5859375000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-454{x}-544$
900.1-f4 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $18.53649180$ $2.808889283$ 4.767964034 \( \frac{35578826569}{5314410} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-69{x}-194$
900.1-f5 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $9.268245903$ $11.23555713$ 4.767964034 \( \frac{702595369}{72900} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-19{x}+26$
900.1-f6 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.089415301$ $1.248395236$ 4.767964034 \( \frac{4102915888729}{9000000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-334{x}-2368$
900.1-f7 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $4.634122951$ $11.23555713$ 4.767964034 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
900.1-f8 900.1-f \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.178830602$ $0.312098809$ 4.767964034 \( \frac{16778985534208729}{81000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$
900.1-g1 900.1-g \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.976308653$ 1.092375998 \( -\frac{2712805671127662691}{777600} a - \frac{4259179431282672263}{388800} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 519 a - 2425\) , \( -20361 a + 85460\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(519a-2425\right){x}-20361a+85460$
900.1-h1 900.1-h \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.518292035$ 1.032716833 \( \frac{2801426243}{540} a + \frac{27291638597}{1620} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -35 a - 115\) , \( -440 a - 1375\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-35a-115\right){x}-440a-1375$
900.1-h2 900.1-h \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.879573008$ 1.032716833 \( \frac{30261551896446437}{150} a + \frac{142534403497790423}{225} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -665 a - 2095\) , \( -20726 a - 65077\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-665a-2095\right){x}-20726a-65077$
900.1-i1 900.1-i \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.929939837$ 0.510948242 \( \frac{769330693747}{468750000} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1330 a + 5556\) , \( 12124 a - 50120\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1330a+5556\right){x}+12124a-50120$
900.1-i2 900.1-i \(\Q(\sqrt{53}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.719759351$ 0.510948242 \( \frac{13094193293}{7200000} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -341 a - 1070\) , \( -2441 a - 7665\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-341a-1070\right){x}-2441a-7665$
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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.