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Results (12 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
5625.2-a1 5625.2-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.859650869$ $0.654920618$ 2.648601831 \( -\frac{102400}{3} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -208\) , \( -1256\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-208{x}-1256$
5625.2-a2 5625.2-a \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $0.571930173$ $3.274603091$ 2.648601831 \( \frac{20480}{243} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$
5625.2-b1 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.537222968$ $0.111785085$ 5.435423749 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2751{x}-104477$
5625.2-b2 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.148891872$ $1.788561370$ 5.435423749 \( -\frac{1}{15} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$
5625.2-b3 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.297783744$ $0.223570171$ 5.435423749 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 874\) , \( -5227\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+874{x}-5227$
5625.2-b4 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.148891872$ $0.447140342$ 5.435423749 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-251{x}-727$
5625.2-b5 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.297783744$ $0.894280685$ 5.435423749 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( 523\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-126{x}+523$
5625.2-b6 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.074445936$ $0.223570171$ 5.435423749 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$
5625.2-b7 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.595567489$ $0.447140342$ 5.435423749 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -2001\) , \( 34273\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$
5625.2-b8 5625.2-b \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.148891872$ $0.111785085$ 5.435423749 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$
5625.2-c1 5625.2-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.361835155$ $3.274603091$ 5.026962901 \( -\frac{102400}{3} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}-8{x}-7$
5625.2-c2 5625.2-c \(\Q(\sqrt{-2}) \) \( 3^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.809175777$ $0.654920618$ 5.026962901 \( \frac{20480}{243} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 42\) , \( 443\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+42{x}+443$
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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.