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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
300.1-a7 300.1-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.747258760 \( \frac{2656166199049}{33750} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -289 a + 288\) , \( 1862\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-289a+288\right){x}+1862$
450.2-a7 450.2-a \(\Q(\sqrt{-1}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.647145070 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.168446869$ $0.970717605$ 1.060794864 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
450.2-a7 450.2-a \(\Q(\sqrt{-2}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.372802002 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 2.341458962 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-289{x}+1862$
60.2-a11 60.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3 \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.668368554 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-19}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $8.724337059$ $0.970717605$ 2.590521960 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.2-a7 90.2-a \(\Q(\sqrt{-5}) \) \( 2 \cdot 3^{2} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.792470734$ $0.970717605$ 1.556288016 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-23}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.619268901 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
150.2-a7 150.2-a \(\Q(\sqrt{-6}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.528391737 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-31}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $2$ $\Z/6\Z$ $\mathrm{SU}(2)$ $5.319170684$ $0.970717605$ 2.473003425 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
180.2-b7 180.2-b \(\Q(\sqrt{-35}) \) \( 2^{2} \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 2.625299565 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
300.5-a7 300.5-a \(\Q(\sqrt{-39}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.829009162 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.1-a7 90.1-a \(\Q(\sqrt{-10}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.409290479 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.1-a7 900.1-a \(\Q(\sqrt{-43}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 3.552793127 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-47}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.132749721 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
300.2-b7 300.2-b \(\Q(\sqrt{-51}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $13.99980317$ $0.970717605$ 5.074561033 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
450.1-a7 450.1-a \(\Q(\sqrt{-13}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $6.699475458$ $0.970717605$ 2.404920737 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
180.2-a7 180.2-a \(\Q(\sqrt{-55}) \) \( 2^{2} \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.698088187 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
450.5-b7 450.5-b \(\Q(\sqrt{-14}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $3.515783703$ $0.970717605$ 3.648472090 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-59}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.011013343 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.1-a7 900.1-a \(\Q(\sqrt{-67}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 2.846208731 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
450.2-d7 450.2-d \(\Q(\sqrt{-17}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.883468809 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.14-g7 900.14-g \(\Q(\sqrt{-71}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.885263529$ $0.970717605$ 3.475007775 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.5-a7 900.5-a \(\Q(\sqrt{-79}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.164952141 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-83}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $19.22664628$ $0.970717605$ 8.194404306 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
150.2-b7 150.2-b \(\Q(\sqrt{-21}) \) \( 2 \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.129749055 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
300.2-a7 300.2-a \(\Q(\sqrt{-87}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.311115244$ $0.970717605$ 2.565568447 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
450.1-a7 450.1-a \(\Q(\sqrt{-22}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $0 \le r \le 1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 4.163573334 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-91}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.947681011$ $0.970717605$ 4.228134163 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
180.5-a7 180.5-a \(\Q(\sqrt{-95}) \) \( 2^{2} \cdot 3^{2} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $4.716986409$ $0.970717605$ 3.758250427 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-103}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $15.26501558$ $0.970717605$ 1.946750444 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
450.5-b7 450.5-b \(\Q(\sqrt{-26}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.471334243$ $0.970717605$ 4.481646086 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.2-a7 900.2-a \(\Q(\sqrt{-107}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $31.22728055$ $0.970717605$ 11.72182339 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
300.5-a7 300.5-a \(\Q(\sqrt{-111}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.941435210$ 0.491394334 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
180.1-b7 180.1-b \(\Q(\sqrt{-115}) \) \( 2^{2} \cdot 3^{2} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $16.59436073$ $0.970717605$ 4.005652265 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.14-j7 900.14-j \(\Q(\sqrt{-119}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.659528350$ $1.941435210$ 3.786552934 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
30.1-f7 30.1-f \(\Q(\sqrt{-30}) \) \( 2 \cdot 3 \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.890431748 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
900.1-a7 900.1-a \(\Q(\sqrt{-163}) \) \( 2^{2} \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.824779299 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
60.1-d7 60.1-d \(\Q(\sqrt{-195}) \) \( 2^{2} \cdot 3 \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $13.69134639$ $0.970717605$ 5.075986833 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
60.2-d7 60.2-d \(\Q(\sqrt{-255}) \) \( 2^{2} \cdot 3 \cdot 5 \) $2$ $\Z/6\Z$ $\mathrm{SU}(2)$ $26.74493920$ $0.970717605$ 4.335439830 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.2-b7 90.2-b \(\Q(\sqrt{-65}) \) \( 2 \cdot 3^{2} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $6.377386154$ $0.970717605$ 6.142836122 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.1-d7 90.1-d \(\Q(\sqrt{-70}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 0.618789041 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.1-a7 90.1-a \(\Q(\sqrt{-85}) \) \( 2 \cdot 3^{2} \cdot 5 \) $0 \le r \le 2$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 2.246167621 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
30.1-c7 30.1-c \(\Q(\sqrt{-105}) \) \( 2 \cdot 3 \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.970717605$ 1.010478273 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
60.1-c7 60.1-c \(\Q(\sqrt{-435}) \) \( 2^{2} \cdot 3 \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $8.661265847$ $0.970717605$ 8.599800291 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.2-b7 90.2-b \(\Q(\sqrt{-110}) \) \( 2 \cdot 3^{2} \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $6.309570797$ $0.970717605$ 4.671822870 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.1-a7 90.1-a \(\Q(\sqrt{-130}) \) \( 2 \cdot 3^{2} \cdot 5 \) $0 \le r \le 2$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.941435210$ 1.816268075 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
60.1-c7 60.1-c \(\Q(\sqrt{-555}) \) \( 2^{2} \cdot 3 \cdot 5 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $45.33905904$ $1.941435210$ 9.963631230 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
90.1-a7 90.1-a \(\Q(\sqrt{-145}) \) \( 2 \cdot 3^{2} \cdot 5 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $1.941435210$ 0.429939783 \( \frac{2656166199049}{33750} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-289{x}+1862$
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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.