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Base field Conductor norm Rank* Torsion order CM discriminant
Base field degree/signature Bad \(p\) $\Q$-curves Torsion structure CM
Analytic order of Ш* Cyclic isogeny degree Isogeny class size Reduction Galois image
Base change of Regulator* Curves per isogeny class Isogeny class degree Nonmax$\ \ell$
j-invariant
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Results (1-50 of 123 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
81.1-CMa1 81.1-CMa \(\Q(\sqrt{-3}) \) \( 3^{4} \) 0 $\Z/3\Z\oplus\Z/3\Z$ $-3$ $\mathrm{U}(1)$ $1$ $8.108628264$ 0.346779163 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
729.1-a3 729.1-a \(\Q(\sqrt{-1}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.900958696 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
729.1-a3 729.1-a \(\Q(\sqrt{-7}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.681060757 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
729.4-b3 729.4-b \(\Q(\sqrt{-2}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1.349576835$ $8.108628264$ 1.719560635 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
729.4-a3 729.4-a \(\Q(\sqrt{-11}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1.571787496$ $8.108628264$ 1.707899690 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}$
81.1-a3 81.1-a \(\Q(\sqrt{-15}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1.216773260$ $8.108628264$ 1.132214990 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-19}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.413388200 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a3 729.4-a \(\Q(\sqrt{-5}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $3.118107923$ $8.108628264$ 2.512702187 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-c4 729.4-c \(\Q(\sqrt{-23}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $3.391021540$ $8.108628264$ 2.548188217 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-6}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $2.263730709$ $8.108628264$ 1.665267531 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-b4 729.1-b \(\Q(\sqrt{-31}) \) \( 3^{6} \) $2$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $3.009274303$ $8.108628264$ 3.895612925 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-35}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $4.854482209$ $8.108628264$ 2.957152791 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-39}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.865613115 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-10}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 1.139632622 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-43}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 1.099159304 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a3 729.4-a \(\Q(\sqrt{-47}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $4.692411943$ $8.108628264$ 2.466675812 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-51}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $4.245720553$ $8.108628264$ 2.142551111 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-13}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.249880982 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a3 729.1-a \(\Q(\sqrt{-55}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.971881966 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-d4 729.4-d \(\Q(\sqrt{-14}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $7.911362464$ $8.108628264$ 3.809975138 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-59}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $3.931045340$ $8.108628264$ 1.844365202 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a3 729.1-a \(\Q(\sqrt{-67}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.220139246 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-17}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $9.700410033$ $8.108628264$ 4.239362057 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-71}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $6.200810795$ $8.108628264$ 2.652065087 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-79}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.202731545 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-83}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $6.678624801$ $8.108628264$ 2.641878694 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-21}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.589815917 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-87}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $6.604668649$ $8.108628264$ 2.551856687 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-b3 729.1-b \(\Q(\sqrt{-22}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.768340157 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a4 729.1-a \(\Q(\sqrt{-91}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.188892267 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-b4 729.4-b \(\Q(\sqrt{-95}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $11.51118954$ $8.108628264$ 4.256212231 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a3 729.1-a \(\Q(\sqrt{-103}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.177548196 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-b4 729.4-b \(\Q(\sqrt{-26}) \) \( 3^{6} \) $0 \le r \le 1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 4.659185008 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-a4 729.4-a \(\Q(\sqrt{-107}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1.226691149$ $8.108628264$ 3.846367046 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-111}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.513091290 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-b3 729.1-b \(\Q(\sqrt{-115}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.672118652 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.4-e4 729.4-e \(\Q(\sqrt{-119}) \) \( 3^{6} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $8.664075157$ $16.21725652$ 2.862289800 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-30}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 1.973901604 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-123}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $8.322549407$ $8.108628264$ 2.704386125 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b3 81.1-b \(\Q(\sqrt{-33}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $9.078865602$ $8.108628264$ 2.847800056 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-159}) \) \( 3^{4} \) $0 \le r \le 1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 3.365982008 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
729.1-a3 729.1-a \(\Q(\sqrt{-163}) \) \( 3^{6} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.141137062 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b3 81.1-b \(\Q(\sqrt{-42}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $15.65311100$ $8.108628264$ 4.352220566 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-183}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.399604699 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a4 81.1-a \(\Q(\sqrt{-219}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.365286880 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b4 81.1-b \(\Q(\sqrt{-57}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 0.358004683 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b4 81.1-b \(\Q(\sqrt{-231}) \) \( 3^{4} \) $1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $13.86125775$ $8.108628264$ 3.286711030 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b4 81.1-b \(\Q(\sqrt{-66}) \) \( 3^{4} \) 0 $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 1.330804190 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-a3 81.1-a \(\Q(\sqrt{-267}) \) \( 3^{4} \) $0 \le r \le 1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 3.047052003 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
81.1-b4 81.1-b \(\Q(\sqrt{-69}) \) \( 3^{4} \) $0 \le r \le 1$ $\Z/3\Z$ $-3$ $N(\mathrm{U}(1))$ $1$ $8.108628264$ 4.076958229 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{y}={x}^3$
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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.