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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
j-invariant Regulator* Curves per isogeny class Isogeny class degree Nonmax$\ \ell$
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Results (4 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
29.1-a1 29.1-a 4.4.2225.1 \( 29 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $288.9003314$ 1.531168694 \( -\frac{4012734681}{58} a^{3} + \frac{11061704843}{58} a^{2} + \frac{632240383}{58} a - \frac{4568350499}{29} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 2\) , \( a^{2} - 3\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - 1\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{3}{2}a^{2}+\frac{3}{2}a-2\right){x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{1}{2}a-3\right){x}+\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+\frac{1}{2}a-1$
29.1-a2 29.1-a 4.4.2225.1 \( 29 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $288.9003314$ 1.531168694 \( \frac{99932939}{58} a^{3} - \frac{19709445}{58} a^{2} - \frac{250236317}{58} a + \frac{81455477}{29} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{17}{2} a - 4\) , \( 6 a^{3} - 29 a - 20\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{3}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(\frac{3}{2}a^{3}-\frac{1}{2}a^{2}-\frac{17}{2}a-4\right){x}+6a^{3}-29a-20$
29.1-a3 29.1-a 4.4.2225.1 \( 29 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $577.8006629$ 1.531168694 \( -\frac{539857941}{1682} a^{3} - \frac{63606739}{1682} a^{2} + \frac{2596822069}{1682} a + \frac{940066182}{841} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 3 a^{3} - 6 a^{2} - 3 a - 1\) , \( \frac{19}{2} a^{3} - \frac{47}{2} a^{2} - \frac{15}{2} a + 20\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(3a^{3}-6a^{2}-3a-1\right){x}+\frac{19}{2}a^{3}-\frac{47}{2}a^{2}-\frac{15}{2}a+20$
29.1-a4 29.1-a 4.4.2225.1 \( 29 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $144.4501657$ 1.531168694 \( -\frac{1061759562256497759}{1414562} a^{3} - \frac{147121931256461299}{1414562} a^{2} + \frac{5141290037660975785}{1414562} a + \frac{1865084993977686479}{707281} \) \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{21}{2} a^{3} - \frac{47}{2} a^{2} - \frac{31}{2} a + 24\) , \( -8 a^{3} + 26 a^{2} - 9 a - 17\bigr] \) ${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-2\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(\frac{21}{2}a^{3}-\frac{47}{2}a^{2}-\frac{31}{2}a+24\right){x}-8a^{3}+26a^{2}-9a-17$
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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.