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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
43.2-a1 43.2-a \(\Q(\zeta_{11})^+\) \( 43 \) 0 $\Z/7\Z$ $\mathrm{SU}(2)$ $1$ $5702.693977$ 0.961830659 \( \frac{411648986}{43} a^{4} + \frac{127511713}{43} a^{3} - 34409287 a^{2} - \frac{702973344}{43} a + \frac{314269044}{43} \) \( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 2 a^{4} + 2 a^{3} - 5 a^{2} - 3 a + 2\) , \( 2 a^{4} + 3 a^{3} - 5 a^{2} - 4 a + 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a-1\right){x}^{2}+\left(2a^{4}+2a^{3}-5a^{2}-3a+2\right){x}+2a^{4}+3a^{3}-5a^{2}-4a+1$
43.2-a2 43.2-a \(\Q(\zeta_{11})^+\) \( 43 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.339304693$ 0.961830659 \( -\frac{70548898331353450135096255010}{271818611107} a^{4} + \frac{189247840974084378816217200685}{271818611107} a^{3} - \frac{842216448583260989645063883}{6321363049} a^{2} - \frac{150714011772341855278459782553}{271818611107} a + \frac{41930794528416841925025385323}{271818611107} \) \( \bigl[a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -a^{4} + 4 a^{2} + a - 3\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a + 1\) , \( -30 a^{4} + 30 a^{3} + 25 a^{2} + 160 a - 215\) , \( -226 a^{4} + 563 a^{3} - 458 a^{2} + 913 a - 1012\bigr] \) ${y}^2+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-3\right){x}^{2}+\left(-30a^{4}+30a^{3}+25a^{2}+160a-215\right){x}-226a^{4}+563a^{3}-458a^{2}+913a-1012$
43.2-b1 43.2-b \(\Q(\zeta_{11})^+\) \( 43 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $537.8461822$ 0.889001954 \( \frac{245417473145}{147008443} a^{4} - \frac{392753447771}{147008443} a^{3} - \frac{61634765294}{3418801} a^{2} - \frac{2240734555627}{147008443} a - \frac{148495909040}{147008443} \) \( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a + 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( -6 a^{4} - a^{3} + 20 a^{2} + 4 a - 8\) , \( -6 a^{4} + a^{3} + 23 a^{2} - 3 a - 15\bigr] \) ${y}^2+\left(a^{4}-3a^{2}+1\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+3a^{2}+4a+1\right){x}^{2}+\left(-6a^{4}-a^{3}+20a^{2}+4a-8\right){x}-6a^{4}+a^{3}+23a^{2}-3a-15$
43.2-b2 43.2-b \(\Q(\zeta_{11})^+\) \( 43 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.172110778$ 0.889001954 \( \frac{4812587720746597807871802}{43} a^{4} + \frac{1490861393846022143062456}{43} a^{3} - 402277955305458024909373 a^{2} - \frac{8218995683117457123881082}{43} a + \frac{3673708517361273227425946}{43} \) \( \bigl[a^{3} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a^{4} - 4 a^{2} + 2\) , \( 42 a^{4} - 193 a^{3} + 148 a^{2} + 559 a - 755\) , \( 589 a^{4} - 2716 a^{3} + 1086 a^{2} + 7676 a - 7875\bigr] \) ${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(42a^{4}-193a^{3}+148a^{2}+559a-755\right){x}+589a^{4}-2716a^{3}+1086a^{2}+7676a-7875$
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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.