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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
1.1-a1 1.1-a \(\Q(\zeta_{13})^+\) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.002671646$ 0.571393 \( -3387888351672962316333 a^{4} + 3387888351672962316333 a^{3} + 13551553406691849265332 a^{2} - 6775776703345924632666 a - 14577323462934449612494 \) \( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( -a^{5} + 6 a^{3} - 8 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -6649 a^{5} + 3526 a^{4} + 36471 a^{3} - 7581 a^{2} - 48724 a - 11069\) , \( -549202 a^{5} + 227195 a^{4} + 2939749 a^{3} - 400010 a^{2} - 3734843 a - 839159\bigr] \) ${y}^2+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-8a+1\right){x}^{2}+\left(-6649a^{5}+3526a^{4}+36471a^{3}-7581a^{2}-48724a-11069\right){x}-549202a^{5}+227195a^{4}+2939749a^{3}-400010a^{2}-3734843a-839159$
1.1-a2 1.1-a \(\Q(\zeta_{13})^+\) \( 1 \) 0 $\Z/19\Z$ $\mathrm{SU}(2)$ $1$ $125689.9848$ 0.571393 \( -17787 a^{4} + 17787 a^{3} + 71148 a^{2} - 35574 a - 75349 \) \( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 3\) , \( 5 a^{5} - 18 a^{3} + 2 a^{2} + 12 a\) , \( 8 a^{5} + 4 a^{4} - 27 a^{3} - 7 a^{2} + 16 a + 1\bigr] \) ${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+3\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+5a\right){x}^{2}+\left(5a^{5}-18a^{3}+2a^{2}+12a\right){x}+8a^{5}+4a^{4}-27a^{3}-7a^{2}+16a+1$
1.1-a3 1.1-a \(\Q(\zeta_{13})^+\) \( 1 \) 0 $\Z/19\Z$ $\mathrm{SU}(2)$ $1$ $125689.9848$ 0.571393 \( 17787 a^{4} - 17787 a^{3} - 71148 a^{2} + 35574 a + 13586 \) \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{5} + 6 a^{3} + a^{2} - 8 a - 1\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( 2 a^{5} - 9 a^{3} + 9 a + 3\) , \( a^{4} + a^{3} - 2 a^{2} - 3 a - 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-8a-1\right){x}^{2}+\left(2a^{5}-9a^{3}+9a+3\right){x}+a^{4}+a^{3}-2a^{2}-3a-1$
1.1-a4 1.1-a \(\Q(\zeta_{13})^+\) \( 1 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.002671646$ 0.571393 \( 3387888351672962316333 a^{4} - 3387888351672962316333 a^{3} - 13551553406691849265332 a^{2} + 6775776703345924632666 a + 2362118295430361969171 \) \( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 6 a + 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 5\) , \( a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 6 a + 1\) , \( 9022 a^{5} + 849 a^{4} - 39313 a^{3} - 5670 a^{2} + 26993 a - 4629\) , \( 611845 a^{5} + 158368 a^{4} - 2641015 a^{3} - 821368 a^{2} + 1693284 a - 462\bigr] \) ${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+6a+2\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-5\right){x}^{2}+\left(9022a^{5}+849a^{4}-39313a^{3}-5670a^{2}+26993a-4629\right){x}+611845a^{5}+158368a^{4}-2641015a^{3}-821368a^{2}+1693284a-462$
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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.