## Results (1-50 of 70040 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
9.1-CMa1 9.1-CMa $$\Q(\sqrt{-2})$$ $$3^{2}$$ $0$ $\Z/6\Z$ $-8$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$
9.3-CMa1 9.3-CMa $$\Q(\sqrt{-2})$$ $$3^{2}$$ $0$ $\Z/6\Z$ $-8$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$
32.1-a1 32.1-a $$\Q(\sqrt{-2})$$ $$2^{5}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ ${y}^2={x}^{3}-{x}$
32.1-a2 32.1-a $$\Q(\sqrt{-2})$$ $$2^{5}$$ $0$ $\Z/4\Z$ $-4$ ${y}^2={x}^{3}+{x}$
32.1-a3 32.1-a $$\Q(\sqrt{-2})$$ $$2^{5}$$ $0$ $\Z/4\Z$ $-16$ ${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}+3$
32.1-a4 32.1-a $$\Q(\sqrt{-2})$$ $$2^{5}$$ $0$ $\Z/4\Z$ $-16$ ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}$
51.1-a1 51.1-a $$\Q(\sqrt{-2})$$ $$3 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
51.1-a2 51.1-a $$\Q(\sqrt{-2})$$ $$3 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+2\right){x}$
51.4-a1 51.4-a $$\Q(\sqrt{-2})$$ $$3 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}$
51.4-a2 51.4-a $$\Q(\sqrt{-2})$$ $$3 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-a$
54.1-a1 54.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}-1$
54.1-a2 54.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$
54.1-a3 54.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+69\right){x}+62a+339$
54.1-a4 54.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+4\right){x}-26$
54.4-a1 54.4-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-1\right){x}-1$
54.4-a2 54.4-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$
54.4-a3 54.4-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(51a+69\right){x}-62a+339$
54.4-a4 54.4-a $$\Q(\sqrt{-2})$$ $$2 \cdot 3^{3}$$ $0$ $\Z/3\Z$ ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+4\right){x}-26$
72.2-a1 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+5{x}+23$
72.2-a2 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/4\Z$ ${y}^2={x}^{3}-{x}^{2}+{x}$
72.2-a3 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
72.2-a4 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}+5$
72.2-a5 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(70a+85\right){x}-98a+559$
72.2-a6 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-70a+85\right){x}+98a+559$
72.2-a7 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-15{x}-27$
72.2-a8 72.2-a $$\Q(\sqrt{-2})$$ $$2^{3} \cdot 3^{2}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-95{x}+347$
98.1-a1 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
98.1-a2 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-{x}$
98.1-a3 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
98.1-a4 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
98.1-a5 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/6\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
98.1-a6 98.1-a $$\Q(\sqrt{-2})$$ $$2 \cdot 7^{2}$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
99.3-a1 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-90\right){x}+71a+302$
99.3-a2 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+95\right){x}+251a-30$
99.3-a3 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}+a+4$
99.3-a4 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
99.3-a5 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+8a{x}+19a+22$
99.3-a6 99.3-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(173a-15\right){x}+859a+1006$
99.4-a1 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(10a-90\right){x}-72a+302$
99.4-a2 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a+95\right){x}-252a-30$
99.4-a3 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-2a+4$
99.4-a4 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/4\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
99.4-a5 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-10a{x}-20a+22$
99.4-a6 99.4-a $$\Q(\sqrt{-2})$$ $$3^{2} \cdot 11$$ $0$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-175a-15\right){x}-860a+1006$
100.1-a1 100.1-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}-8{x}+18$
100.1-a2 100.1-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 5^{2}$$ $1$ $\Z/6\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+2{x}$
100.1-a3 100.1-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 5^{2}$$ $1$ $\Z/6\Z$ ${y}^2={x}^{3}+{x}^{2}-{x}$
100.1-a4 100.1-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 5^{2}$$ $1$ $\Z/2\Z$ ${y}^2={x}^{3}+{x}^{2}-41{x}-116$
108.2-a1 108.2-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 3^{3}$$ $0$ $\Z/4\Z$ ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a+4\right){x}+122a-261$
108.2-a2 108.2-a $$\Q(\sqrt{-2})$$ $$2^{2} \cdot 3^{3}$$ $0$ $\Z/6\Z$ ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a+49\right){x}+7a+265$