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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3872.14-b3 3872.14-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.730960613$ 2.210217144 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 69 a + 153\) , \( 753 a - 1067\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(69a+153\right){x}+753a-1067$
3872.5-b3 3872.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.730960613$ 2.210217144 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -102 a - 107\) , \( 867 a + 190\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-102a-107\right){x}+867a+190$
5324.6-e3 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -132 a - 483\) , \( -1724 a - 3749\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-132a-483\right){x}-1724a-3749$
5324.7-d3 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 329 a + 211\) , \( -1214 a + 5583\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(329a+211\right){x}-1214a+5583$
15488.20-d4 15488.20-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -292 a - 13\) , \( 2282 a - 1707\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-292a-13\right){x}+2282a-1707$
15488.5-d4 15488.5-d \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.516867206$ 1.562859530 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -4 a + 422\) , \( 2375 a - 1363\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+422\right){x}+2375a-1363$
23716.5-a4 23716.5-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $2$ $\Z/2\Z$ $0.131842497$ $0.552554286$ 3.524449760 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 231 a - 317\) , \( -2079 a + 1315\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(231a-317\right){x}-2079a+1315$
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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.