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Results (6 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
75.1-a6 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 0.856151218 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
75.1-b6 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.086147259$ $10.19195692$ 1.532778450 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 677 a - 1886\) , \( -14484 a + 40430\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(677a-1886\right){x}-14484a+40430$
225.1-a6 225.1-a \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.581565971$ 2.253375518 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 409 a - 1208\) , \( 7111 a - 19743\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(409a-1208\right){x}+7111a-19743$
225.1-b6 225.1-b \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.581565971$ 2.253375518 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -404 a - 807\) , \( -7917 a - 13855\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-404a-807\right){x}-7917a-13855$
1875.1-u6 1875.1-u \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.038391385$ 0.889626935 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 16877 a - 47258\) , \( -1800565 a + 5026434\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(16877a-47258\right){x}-1800565a+5026434$
1875.1-x6 1875.1-x \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.308958211$ $0.392337776$ 3.586131735 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$
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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.