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Results (14 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1764.1-a1 1764.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $1.662392940$ 1.486889448 \( \frac{28849701763}{16941456} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( 64 \phi + 64\) , \( -64 \phi - 48\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(64\phi+64\right){x}-64\phi-48$
1764.1-a2 1764.1-a \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $6.649571763$ 1.486889448 \( \frac{461889917}{263424} \) \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( -16 \phi - 16\) , \( 0\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(-16\phi-16\right){x}$
1764.1-b1 1764.1-b \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.254767849$ 1.455576432 \( -\frac{19375146756295}{1176} a + \frac{47024472265469}{1764} \) \( \bigl[\phi\) , \( 0\) , \( \phi + 1\) , \( -25 \phi - 58\) , \( 82 \phi - 58\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(-25\phi-58\right){x}+82\phi-58$
1764.1-b2 1764.1-b \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $6.509535698$ 1.455576432 \( -\frac{43378775}{1344} a + \frac{232156657}{1344} \) \( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( 4 \phi - 16\) , \( 9 \phi - 26\bigr] \) ${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(4\phi-16\right){x}+9\phi-26$
1764.1-c1 1764.1-c \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $6.509535698$ 1.455576432 \( \frac{43378775}{1344} a + \frac{94388941}{672} \) \( \bigl[1\) , \( 0\) , \( \phi\) , \( -5 \phi - 11\) , \( -10 \phi - 16\bigr] \) ${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(-5\phi-11\right){x}-10\phi-16$
1764.1-c2 1764.1-c \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.254767849$ 1.455576432 \( \frac{19375146756295}{1176} a + \frac{35923504262053}{3528} \) \( \bigl[\phi + 1\) , \( -\phi\) , \( \phi\) , \( 23 \phi - 82\) , \( -83 \phi + 25\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\phi{y}={x}^{3}-\phi{x}^{2}+\left(23\phi-82\right){x}-83\phi+25$
1764.1-d1 1764.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $0.976472467$ 0.873383526 \( -\frac{310288733}{11573604} \) \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -14 \phi - 14\) , \( -314 \phi - 232\bigr] \) ${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(-14\phi-14\right){x}-314\phi-232$
1764.1-d2 1764.1-d \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z$ $1$ $3.905889871$ 0.873383526 \( \frac{4386781853}{27216} \) \( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 33 \phi - 68\) , \( 113 \phi - 208\bigr] \) ${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(33\phi-68\right){x}+113\phi-208$
1764.1-e1 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/8\Z$ $0.697547317$ $12.07873502$ 1.883996662 \( -\frac{7189057}{16128} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$
1764.1-e2 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.348773658$ $0.754920939$ 1.883996662 \( \frac{6359387729183}{4218578658} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+386{x}+1277$
1764.1-e3 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.174386829$ $3.019683757$ 1.883996662 \( \frac{124475734657}{63011844} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$
1764.1-e4 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $0.348773658$ $0.754920939$ 1.883996662 \( \frac{84448510979617}{933897762} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$
1764.1-e5 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.348773658$ $12.07873502$ 1.883996662 \( \frac{65597103937}{63504} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$
1764.1-e6 1764.1-e \(\Q(\sqrt{5}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/4\Z$ $0.697547317$ $12.07873502$ 1.883996662 \( \frac{268498407453697}{252} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-1344{x}+18405$
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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.