## Results (1-50 of 70927 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
16.1-CMa1 16.1-CMa $$\Q(\sqrt{-7})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $-7$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
16.1-CMa2 16.1-CMa $$\Q(\sqrt{-7})$$ $$2^{4}$$ $0$ $\Z/4\Z$ $-28$ ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+11\right){x}-7a+26$
16.5-CMa1 16.5-CMa $$\Q(\sqrt{-7})$$ $$2^{4}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ $-7$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
16.5-CMa2 16.5-CMa $$\Q(\sqrt{-7})$$ $$2^{4}$$ $0$ $\Z/4\Z$ $-28$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-5\right){x}+22a+14$
28.2-a1 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
28.2-a2 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-10a+15\right){x}-5a-16$
28.2-a3 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+6\right){x}+4a-20$
28.2-a4 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a+1$
28.2-a5 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}$
28.2-a6 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-{x}$
28.2-a7 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
28.2-a8 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(30a-40\right){x}-30a-154$
28.2-a9 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-9\right){x}+29a-183$
28.2-a10 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
28.2-a11 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
28.2-a12 28.2-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
44.3-a1 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-55a+91\right){x}+87a+359$
44.3-a2 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4a+40\right){x}+135a+83$
44.3-a3 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/12\Z$ ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$
44.3-a4 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-17\right){x}-19a+5$
44.3-a5 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}+1$
44.3-a6 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14a-10\right){x}+27a-9$
44.3-a7 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+3\right){x}-3a+1$
44.3-a8 44.3-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+21a{x}+20a+57$
44.4-a1 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(55a+36\right){x}-87a+446$
44.4-a2 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3a+37\right){x}-136a+219$
44.4-a3 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/12\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}+1$
44.4-a4 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-14a-3\right){x}+19a-14$
44.4-a5 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a+2\right){x}-a+2$
44.4-a6 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(13a-23\right){x}-28a+19$
44.4-a7 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}+3a-2$
44.4-a8 44.4-a $$\Q(\sqrt{-7})$$ $$2^{2} \cdot 11$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-22a+22\right){x}-21a+78$
46.2-a1 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-1$
46.2-a2 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+10\right){x}+2a+8$
46.2-a3 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+10\right){x}-8a+30$
46.2-a4 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$
46.2-a5 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}-a+1$
46.2-a6 46.2-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-91a+170\right){x}+240a+618$
46.3-a1 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-4\right){x}-a-4$
46.3-a2 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+4\right){x}-3a+10$
46.3-a3 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+9{x}+7a+22$
46.3-a4 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-{x}-a$
46.3-a5 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-2{x}+1$
46.3-a6 46.3-a $$\Q(\sqrt{-7})$$ $$2 \cdot 23$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(90a+79\right){x}-241a+858$
49.1-CMa1 49.1-CMa $$\Q(\sqrt{-7})$$ $$7^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $-7$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
49.1-CMa2 49.1-CMa $$\Q(\sqrt{-7})$$ $$7^{2}$$ $0$ $\Z/2\Z$ $-28$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
63.1-a1 63.1-a $$\Q(\sqrt{-7})$$ $$3^{2} \cdot 7$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}={x}^{3}-34{x}-217$
63.1-a2 63.1-a $$\Q(\sqrt{-7})$$ $$3^{2} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}+{x}$
63.1-a3 63.1-a $$\Q(\sqrt{-7})$$ $$3^{2} \cdot 7$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+{x}{y}={x}^{3}-4{x}-1$
63.1-a4 63.1-a $$\Q(\sqrt{-7})$$ $$3^{2} \cdot 7$$ $0$ $\Z/8\Z$ ${y}^2+{x}{y}={x}^{3}-39{x}+90$