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Results (8 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
275.1-a1 275.1-a \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.540805159$ $16.93058676$ 2.972859409 \( \frac{59319}{55} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$
275.1-a2 275.1-a \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.081610318$ $16.93058676$ 2.972859409 \( \frac{8120601}{3025} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-4{x}+3$
275.1-a3 275.1-a \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.163220637$ $4.232646692$ 2.972859409 \( \frac{2749884201}{73205} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-29{x}-52$
275.1-a4 275.1-a \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.540805159$ $16.93058676$ 2.972859409 \( \frac{22930509321}{6875} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
275.1-b1 275.1-b \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $5.638786672$ $11.85112914$ 1.903882058 \( \frac{59319}{55} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 44\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+44\right){x}$
275.1-b2 275.1-b \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.819393336$ $11.85112914$ 1.903882058 \( \frac{8120601}{3025} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -36 a - 141\) , \( -276 a - 1074\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-36a-141\right){x}-276a-1074$
275.1-b3 275.1-b \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.409696668$ $11.85112914$ 1.903882058 \( \frac{2749884201}{73205} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 261 a - 1276\) , \( -4160 a + 20332\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(261a-1276\right){x}-4160a+20332$
275.1-b4 275.1-b \(\Q(\sqrt{77}) \) \( 5^{2} \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.409696668$ $2.962782285$ 1.903882058 \( \frac{22930509321}{6875} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -531 a - 2066\) , \( -15731 a - 61156\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-531a-2066\right){x}-15731a-61156$
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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.