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Results (16 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
32.1-a1 32.1-a \(\Q(\sqrt{10}) \) \( 2^{5} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.949741086$ $13.75037163$ 2.064855508 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}$
32.1-a2 32.1-a \(\Q(\sqrt{10}) \) \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1.899482172$ $27.50074327$ 2.064855508 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) ${y}^2={x}^{3}-4{x}$
32.1-b1 32.1-b \(\Q(\sqrt{10}) \) \( 2^{5} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $27.50074327$ 1.087062326 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}$
32.1-b2 32.1-b \(\Q(\sqrt{10}) \) \( 2^{5} \) 0 $\Z/4\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $13.75037163$ 1.087062326 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) ${y}^2={x}^{3}+4{x}$
256.1-b1 256.1-b \(\Q(\sqrt{10}) \) \( 2^{8} \) $2$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1.838697222$ $13.75037163$ 3.997556959 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a + 19\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-6a+19\right){x}$
256.1-b2 256.1-b \(\Q(\sqrt{10}) \) \( 2^{8} \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1.838697222$ $27.50074327$ 3.997556959 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 24 a - 76\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(24a-76\right){x}$
256.1-e1 256.1-e \(\Q(\sqrt{10}) \) \( 2^{8} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $13.75037163$ 2.174124652 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a + 76\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-24a+76\right){x}$
256.1-e2 256.1-e \(\Q(\sqrt{10}) \) \( 2^{8} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $27.50074327$ 2.174124652 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 19\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(6a-19\right){x}$
288.2-a1 288.2-a \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $15.87756153$ 2.510462906 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 13\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(4a-13\right){x}$
288.2-a2 288.2-a \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $7.938780765$ 2.510462906 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 52\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-16a+52\right){x}$
288.2-f1 288.2-f \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.492517393$ $7.938780765$ 2.472893293 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 13\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-4a+13\right){x}$
288.2-f2 288.2-f \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.246258696$ $15.87756153$ 2.472893293 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 52\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(16a-52\right){x}$
288.3-a1 288.3-a \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $15.87756153$ 2.510462906 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 13\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-4a-13\right){x}$
288.3-a2 288.3-a \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) 0 $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $1$ $7.938780765$ 2.510462906 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 52\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(16a+52\right){x}$
288.3-f1 288.3-f \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.492517393$ $7.938780765$ 2.472893293 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 13\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(4a+13\right){x}$
288.3-f2 288.3-f \(\Q(\sqrt{10}) \) \( 2^{5} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-4$ $N(\mathrm{U}(1))$ $0.246258696$ $15.87756153$ 2.472893293 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 52\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-16a-52\right){x}$
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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.