## Results (22 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
3872.14-a1 3872.14-a $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-6a+2\right){x}$
3872.14-a2 3872.14-a $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(24a-8\right){x}-18a-26$
3872.14-a3 3872.14-a $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-24\right){x}-22a+46$
3872.14-a4 3872.14-a $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+22\right){x}+26a-14$
3872.14-b1 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-20\right){x}+11a-9$
3872.14-b2 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(9a+13\right){x}+9a+13$
3872.14-b3 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(69a+153\right){x}+753a-1067$
3872.14-b4 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(102a-210\right){x}-765a+847$
3872.14-b5 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(33a+37\right){x}+111a-245$
3872.14-b6 3872.14-b $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(42a-62\right){x}-163a+81$
3872.14-c1 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-471a-938\right){x}-9387a-9491$
3872.14-c2 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a+6\right){x}+5a-73$
3872.14-c3 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(17a-31\right){x}-13a-33$
3872.14-c4 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a-12\right){x}-36a+19$
3872.14-c5 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-58\right){x}-147a-163$
3872.14-c6 3872.14-c $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(157a-351\right){x}+1387a-2265$
3872.14-d1 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(30a+86\right){x}-500a-580$
3872.14-d2 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-113\right){x}-353a-833$
3872.14-d3 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(138a+159\right){x}+623a-1831$
3872.14-d4 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(178a-265\right){x}-1275a+703$
3872.14-d5 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2138a+2479\right){x}+46031a-123975$
3872.14-d6 3872.14-d $$\Q(\sqrt{-7})$$ $$2^{5} \cdot 11^{2}$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2738a-4105\right){x}-87547a+61119$