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## Results (19 matches)

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Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
5324.7-a1 5324.7-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/3\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(44a-37\right){x}+279a-159$
5324.7-a2 5324.7-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-396a+348\right){x}-6354a+6144$
5324.7-b1 5324.7-b $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a+2\right){x}+a+2$
5324.7-c1 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(157a+140\right){x}+3795a-654$
5324.7-c2 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/4\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(48a-320\right){x}+3251a+758$
5324.7-c3 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(537a+109\right){x}+192a+7744$
5324.7-c4 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(307a-849\right){x}+4407a-7821$
5324.7-c5 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(8297a+1789\right){x}+17536a+527872$
5324.7-c6 5324.7-c $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $1$ $\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4707a-13169\right){x}+291111a-525613$
5324.7-d1 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a-64\right){x}-59a+50$
5324.7-d2 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(39a+11\right){x}-46a-37$
5324.7-d3 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(329a+211\right){x}-1214a+5583$
5324.7-d4 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(131a-614\right){x}+1723a-5472$
5324.7-d5 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(129a+23\right){x}+26a+989$
5324.7-d6 5324.7-d $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(75a-202\right){x}+547a-934$
5324.7-e1 5324.7-e $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+12\right){x}+15a-13$
5324.7-e2 5324.7-e $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(66a-58\right){x}+71a+59$
5324.7-e3 5324.7-e $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-54\right){x}-59a-165$
5324.7-e4 5324.7-e $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11^{3}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(16a+46\right){x}-130a+160$
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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.