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## Results (26 matches)

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Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
50700.2-a1 50700.2-a $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-52a+51\right){x}-124$
50700.2-a2 50700.2-a $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-852a+851\right){x}-9084$
50700.2-b1 50700.2-b $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-97a{x}-297$
50700.2-b2 50700.2-b $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+33a{x}-63$
50700.2-b3 50700.2-b $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+13a{x}+13$
50700.2-b4 50700.2-b $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+483a{x}-4293$
50700.2-c1 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-114a+114\right){x}-12978$
50700.2-c2 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(16a-16\right){x}$
50700.2-c3 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-64a+64\right){x}+112$
50700.2-c4 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-564a+564\right){x}-4788$
50700.2-c5 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-844a+844\right){x}+9940$
50700.2-c6 50700.2-c $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-9014a+9014\right){x}-324198$
50700.2-d1 50700.2-d $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-5a{x}-7$
50700.2-d2 50700.2-d $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+45a{x}-127$
50700.2-e1 50700.2-e $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}={x}^{3}-6{x}+36$
50700.2-e2 50700.2-e $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}={x}^{3}+54{x}-960$
50700.2-e3 50700.2-e $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}={x}^{3}-1196{x}-15210$
50700.2-e4 50700.2-e $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}={x}^{3}-206{x}+1116$
50700.2-f1 50700.2-f $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-53378a+53377\right){x}-5124652$
50700.2-f2 50700.2-f $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(3997a-3998\right){x}+3998$
50700.2-f3 50700.2-f $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-16003a+16002\right){x}+27998$
50700.2-f4 50700.2-f $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/6\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-872578a+872577\right){x}-313799212$
50700.2-g1 50700.2-g $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+288a{x}+3092$
50700.2-g2 50700.2-g $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+6208a{x}+104276$
50700.2-g3 50700.2-g $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+5408a{x}+152596$
50700.2-g4 50700.2-g $$\Q(\sqrt{-3})$$ $$2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+86528a{x}+9789652$
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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.