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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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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4.2-b2 4.2-b 4.4.7232.1 \( 2^{2} \) 0 $\Z/22\Z$ $\mathrm{SU}(2)$ $1$ $423.6523509$ 2.490866296 \( \frac{2296475}{512} a^{3} + \frac{11641725}{2048} a^{2} - \frac{3623639}{512} a - \frac{2976765}{512} \) \( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -\frac{5}{2} a^{3} - 4 a^{2} + \frac{5}{2} a + 4\) , \( \frac{13}{2} a^{3} + 6 a^{2} - \frac{25}{2} a - 8\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a-1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-\frac{5}{2}a^{3}-4a^{2}+\frac{5}{2}a+4\right){x}+\frac{13}{2}a^{3}+6a^{2}-\frac{25}{2}a-8$
4.2-b3 4.2-b 4.4.7232.1 \( 2^{2} \) 0 $\Z/22\Z$ $\mathrm{SU}(2)$ $1$ $423.6523509$ 2.490866296 \( \frac{45730997}{2048} a^{3} - \frac{121475519}{2048} a^{2} - \frac{150256135}{2048} a + \frac{284340953}{2048} \) \( \bigl[a^{2} - a - 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( a^{2} - 2\) , \( -\frac{5}{2} a^{3} + \frac{37}{2} a + 7\) , \( a^{3} - a^{2} - 9 a - 4\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){x}^{2}+\left(-\frac{5}{2}a^{3}+\frac{37}{2}a+7\right){x}+a^{3}-a^{2}-9a-4$
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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.