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Results (9 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
300.1-a8 300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.323572535$ 0.747258760 \( \frac{16778985534208729}{81000} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-5334{x}-150368$
7500.1-b8 7500.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.064714507$ 1.793421026 \( \frac{16778985534208729}{81000} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 133337 a\) , \( -18795969\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+133337a{x}-18795969$
19200.1-e8 19200.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.080893133$ 2.241776282 \( \frac{16778985534208729}{81000} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -85336\) , \( 9623536\bigr] \) ${y}^2={x}^{3}-{x}^{2}-85336{x}+9623536$
44100.1-b8 44100.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.070609315$ 1.956782763 \( \frac{16778985534208729}{81000} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 80005 a + 48001\) , \( -8894060 a + 16610817\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(80005a+48001\right){x}-8894060a+16610817$
44100.3-b8 44100.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.070609315$ 1.956782763 \( \frac{16778985534208729}{81000} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -48002 a - 80003\) , \( 9022065 a + 7668755\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-48002a-80003\right){x}+9022065a+7668755$
50700.1-b8 50700.1-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.572934406$ $0.089742874$ 2.724511424 \( \frac{16778985534208729}{81000} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 80002 a - 37335\) , \( -5413239 a - 2556252\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(80002a-37335\right){x}-5413239a-2556252$
50700.3-b8 50700.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.572934406$ $0.089742874$ 2.724511424 \( \frac{16778985534208729}{81000} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -80003 a + 42668\) , \( 5413239 a - 7969491\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-80003a+42668\right){x}+5413239a-7969491$
57600.1-a8 57600.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $17.12567554$ $0.046703672$ 3.694265501 \( \frac{16778985534208729}{81000} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -256008 a\) , \( 57741216 a - 28870608\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-256008a{x}+57741216a-28870608$
57600.1-p8 57600.1-p \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $17.12567554$ $0.046703672$ 3.694265501 \( \frac{16778985534208729}{81000} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -256008 a\) , \( -57741216 a + 28870608\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-256008a{x}-57741216a+28870608$
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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.