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Results (27 matches)

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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
11.1-a3 11.1-a \(\Q(\sqrt{-11}) \) \( 11 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $9.257718117$ 0.446609125 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}$
275.1-a3 275.1-a \(\Q(\sqrt{-11}) \) \( 5^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.164896198$ $4.140177405$ 1.646733189 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 0\) , \( a - 3\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a-3$
275.3-a3 275.3-a \(\Q(\sqrt{-11}) \) \( 5^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.164896198$ $4.140177405$ 1.646733189 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2 a - 1\) , \( -3\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}-3$
891.3-d3 891.3-d \(\Q(\sqrt{-11}) \) \( 3^{4} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.306230066$ $3.085906039$ 2.279419039 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) ${y}^2+{y}={x}^{3}-3{x}-5$
1089.1-c3 1089.1-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.390608897$ $1.611561869$ 3.036775978 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a\) , \( 1\) , \( 4 a - 12\) , \( -18 a + 25\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(4a-12\right){x}-18a+25$
1089.3-c3 1089.3-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.390608897$ $1.611561869$ 3.036775978 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -4 a - 8\) , \( 18 a + 7\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-8\right){x}+18a+7$
2816.1-c3 2816.1-c \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.882972080$ $2.314429529$ 4.929292363 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -5\) , \( -13\bigr] \) ${y}^2={x}^{3}+{x}^{2}-5{x}-13$
6875.3-b3 6875.3-b \(\Q(\sqrt{-11}) \) \( 5^{4} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.851543623$ 2.233045629 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -8\) , \( 19\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-8{x}+19$
15059.1-a3 15059.1-a \(\Q(\sqrt{-11}) \) \( 11 \cdot 37^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.521959483$ 1.835552200 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -7 a + 8\) , \( 4 a - 39\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-7a+8\right){x}+4a-39$
15059.3-a3 15059.3-a \(\Q(\sqrt{-11}) \) \( 11 \cdot 37^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.521959483$ 1.835552200 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 7 a + 1\) , \( -4 a - 35\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(7a+1\right){x}-4a-35$
22275.7-i3 22275.7-i \(\Q(\sqrt{-11}) \) \( 3^{4} \cdot 5^{2} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.380059135$ 1.664413941 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -9 a + 6\) , \( -19 a + 52\bigr] \) ${y}^2+{y}={x}^{3}+\left(-9a+6\right){x}-19a+52$
22275.9-i3 22275.9-i \(\Q(\sqrt{-11}) \) \( 3^{4} \cdot 5^{2} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.380059135$ 1.664413941 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 9 a - 3\) , \( 19 a + 33\bigr] \) ${y}^2+{y}={x}^{3}+\left(9a-3\right){x}+19a+33$
25344.1-j3 25344.1-j \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 3^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.161809716$ $1.336236511$ 3.744656477 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a + 15\) , \( -26 a - 39\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-5a+15\right){x}-26a-39$
25344.1-q3 25344.1-q \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 3^{2} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.336236511$ 1.611561869 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 15\) , \( 26 a + 39\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5a+15\right){x}+26a+39$
25344.3-i3 25344.3-i \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 3^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.161809716$ $1.336236511$ 3.744656477 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a + 10\) , \( 26 a - 65\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+10\right){x}+26a-65$
25344.3-p3 25344.3-p \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 3^{2} \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.336236511$ 1.611561869 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 5 a + 10\) , \( -26 a + 65\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+10\right){x}-26a+65$
26411.1-c3 26411.1-c \(\Q(\sqrt{-11}) \) \( 7^{4} \cdot 11 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.391843182$ $1.322531159$ 10.00004236 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -16\) , \( -66\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-16{x}-66$
27225.1-c3 27225.1-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.948964364$ $0.720712377$ 3.299404216 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -29 a - 12\) , \( 238 a - 163\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-29a-12\right){x}+238a-163$
27225.3-e3 27225.3-e \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.914519372$ $0.720712377$ 6.656491569 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a\) , \( 1\) , \( 26 a + 21\) , \( 70 a - 415\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(26a+21\right){x}+70a-415$
27225.7-e3 27225.7-e \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.914519372$ $0.720712377$ 6.656491569 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -26 a + 47\) , \( -70 a - 345\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-26a+47\right){x}-70a-345$
27225.9-c3 27225.9-c \(\Q(\sqrt{-11}) \) \( 3^{2} \cdot 5^{2} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.948964364$ $0.720712377$ 3.299404216 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 29 a - 41\) , \( -238 a + 75\bigr] \) ${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-41\right){x}-238a+75$
30899.1-a3 30899.1-a \(\Q(\sqrt{-11}) \) \( 11 \cdot 53^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.348638106$ $1.271645381$ 8.555088456 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 9 a + 7\) , \( 20 a - 77\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(9a+7\right){x}+20a-77$
30899.3-a3 30899.3-a \(\Q(\sqrt{-11}) \) \( 11 \cdot 53^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.348638106$ $1.271645381$ 8.555088456 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -7 a + 15\) , \( -12 a - 72\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+15\right){x}-12a-72$
30976.1-j3 30976.1-j \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.976358665$ $0.697826759$ 3.286855747 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 58\) , \( 228 a - 143\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+58\right){x}+228a-143$
30976.1-o3 30976.1-o \(\Q(\sqrt{-11}) \) \( 2^{8} \cdot 11^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.976358665$ $0.697826759$ 3.286855747 \( -\frac{4096}{11} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 58\) , \( -228 a + 143\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+58\right){x}-228a+143$
45056.1-e3 45056.1-e \(\Q(\sqrt{-11}) \) \( 2^{12} \cdot 11 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.244890052$ $4.628859058$ 5.468506622 \( -\frac{4096}{11} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \) ${y}^2={x}^{3}-{x}^{2}-{x}-1$
45056.1-n3 45056.1-n \(\Q(\sqrt{-11}) \) \( 2^{12} \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.507203009$ $4.628859058$ 5.663037319 \( -\frac{4096}{11} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) ${y}^2={x}^{3}+{x}^{2}-{x}+1$
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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.