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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
25.2-d1 25.2-d \(\Q(\sqrt{6}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 1.499537701 \( 0 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -192 a - 470\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-192a-470$
25.2-d2 25.2-d \(\Q(\sqrt{6}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 1.499537701 \( 0 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( a - 5\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+a-5$
25.3-d1 25.3-d \(\Q(\sqrt{6}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 1.499537701 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 192 a - 470\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+192a-470$
25.3-d2 25.3-d \(\Q(\sqrt{6}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 1.499537701 \( 0 \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -2 a - 5\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-2a-5$
36.1-a1 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $5.898343969$ 1.203994421 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a - 485\bigr] \) ${y}^2={x}^{3}+198a-485$
36.1-a2 36.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.69503190$ 1.203994421 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) ${y}^2={x}^{3}+1$
81.1-b3 81.1-b \(\Q(\sqrt{6}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $0.449858945$ $28.08911226$ 1.719560635 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
81.1-b4 81.1-b \(\Q(\sqrt{6}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1.349576835$ $9.363037422$ 1.719560635 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 49 a - 123\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+49a-123$
100.2-a1 100.2-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.199657850$ $17.04903024$ 1.389666049 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -2\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-2$
100.2-a2 100.2-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.066552616$ $17.04903024$ 1.389666049 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -9 a - 23\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-9a-23$
100.2-b1 100.2-b \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1.276191853$ $7.913458842$ 2.061468462 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 50 a - 123\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}+50a-123$
100.2-b2 100.2-b \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.425397284$ $7.913458842$ 2.061468462 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -4 a - 9\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}-4a-9$
100.3-a1 100.3-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.199657850$ $17.04903024$ 1.389666049 \( 0 \) \( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( -2\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}-2$
100.3-a2 100.3-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.066552616$ $17.04903024$ 1.389666049 \( 0 \) \( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( 9 a - 23\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}+9a-23$
100.3-b1 100.3-b \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1.276191853$ $7.913458842$ 2.061468462 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -50 a - 123\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}-50a-123$
100.3-b2 100.3-b \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.425397284$ $7.913458842$ 2.061468462 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 4 a - 9\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}+4a-9$
144.1-c1 144.1-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.489926008$ $5.898343969$ 2.359472722 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) ${y}^2={x}^{3}-1$
144.1-c2 144.1-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 3^{2} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.163308669$ $17.69503190$ 2.359472722 \( 0 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 198 a + 485\bigr] \) ${y}^2={x}^{3}+198a+485$
225.2-i1 225.2-i \(\Q(\sqrt{6}) \) \( 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $5.475537501$ 1.117689412 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 6 a - 15\bigr] \) ${y}^2+{y}={x}^{3}+6a-15$
225.2-i2 225.2-i \(\Q(\sqrt{6}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $16.42661250$ 1.117689412 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 10 a + 24\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+10a+24$
225.3-i1 225.3-i \(\Q(\sqrt{6}) \) \( 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $5.475537501$ 1.117689412 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -6 a - 15\bigr] \) ${y}^2+{y}={x}^{3}-6a-15$
225.3-i2 225.3-i \(\Q(\sqrt{6}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $16.42661250$ 1.117689412 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -11 a + 24\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-11a+24$
256.1-c1 256.1-c \(\Q(\sqrt{6}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $2.579744927$ $10.21623143$ 2.689873605 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a - 3\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}-a-3$
256.1-c2 256.1-c \(\Q(\sqrt{6}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.859914975$ $30.64869430$ 2.689873605 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -a + 3\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}-a+3$
256.1-f1 256.1-f \(\Q(\sqrt{6}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $2.579744927$ $10.21623143$ 2.689873605 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a - 3\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}+a-3$
256.1-f2 256.1-f \(\Q(\sqrt{6}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $0.859914975$ $30.64869430$ 2.689873605 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a + 3\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}+a+3$
324.1-a1 324.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{4} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.431447726$ 1.516937915 \( 0 \) \( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -2\bigr] \) ${y}^2+a{y}={x}^{3}-2$
324.1-a2 324.1-a \(\Q(\sqrt{6}) \) \( 2^{2} \cdot 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $22.29434318$ 1.516937915 \( 0 \) \( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 99 a + 241\bigr] \) ${y}^2+a{y}={x}^{3}+99a+241$
400.2-c1 400.2-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.04903024$ 3.480118726 \( 0 \) \( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}-1$
400.2-c2 400.2-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.04903024$ 3.480118726 \( 0 \) \( \bigl[0\) , \( a\) , \( a\) , \( 2\) , \( 9 a + 20\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+2{x}+9a+20$
400.2-e1 400.2-e \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.913458842$ 1.615328022 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 4 a + 9\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}+4a+9$
400.2-e2 400.2-e \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.913458842$ 1.615328022 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -50 a + 123\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}-50a+123$
400.2-g1 400.2-g \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.673102219$ 0.749768850 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( -1534 a - 3758\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}-1534a-3758$
400.2-g2 400.2-g \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.673102219$ 0.749768850 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2\) , \( 14 a - 26\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+2{x}+14a-26$
400.3-c1 400.3-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.04903024$ 3.480118726 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-1$
400.3-c2 400.3-c \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $17.04903024$ 3.480118726 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 2\) , \( -9 a + 20\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+2{x}-9a+20$
400.3-e1 400.3-e \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.913458842$ 1.615328022 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -4 a + 9\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}-4a+9$
400.3-e2 400.3-e \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\Z/2\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.913458842$ 1.615328022 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 50 a + 123\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}+50a+123$
400.3-g1 400.3-g \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.673102219$ 0.749768850 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( 1534 a - 3758\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}+1534a-3758$
400.3-g2 400.3-g \(\Q(\sqrt{6}) \) \( 2^{4} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $3.673102219$ 0.749768850 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( -14 a - 26\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+2{x}-14a-26$
625.1-a1 625.1-a \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.269498295$ $7.346204439$ 1.616491420 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 3 a + 6\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+3a+6$
625.1-a2 625.1-a \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.089832765$ $7.346204439$ 1.616491420 \( 0 \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -110 a + 267\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-110a+267$
625.1-d1 625.1-d \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.891744475$ $7.346204439$ 2.674408923 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 2\) , \( 63 a - 154\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+2{x}+63a-154$
625.1-d2 625.1-d \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.297248158$ $7.346204439$ 2.674408923 \( 0 \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( 2\) , \( -5 a - 13\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+2{x}-5a-13$
625.1-g1 625.1-g \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.891744475$ $7.346204439$ 2.674408923 \( 0 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -63 a - 154\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-63a-154$
625.1-g2 625.1-g \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.297248158$ $7.346204439$ 2.674408923 \( 0 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( 4 a - 13\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+4a-13$
625.1-i1 625.1-i \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.269498295$ $7.346204439$ 1.616491420 \( 0 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 2\) , \( -3 a + 6\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+2{x}-3a+6$
625.1-i2 625.1-i \(\Q(\sqrt{6}) \) \( 5^{4} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.089832765$ $7.346204439$ 1.616491420 \( 0 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 2\) , \( 109 a + 267\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+2{x}+109a+267$
729.1-b1 729.1-b \(\Q(\sqrt{6}) \) \( 3^{6} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.781767729$ $9.363037422$ 2.988263384 \( 0 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a - 3\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a-3$
729.1-b2 729.1-b \(\Q(\sqrt{6}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $2.345303189$ $28.08911226$ 2.988263384 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -5 a + 12\bigr] \) ${y}^2+{y}={x}^{3}-5a+12$
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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.