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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
27075.2-a1 27075.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.047706362$ $1.959065350$ 2.590036220 \( \frac{357911}{135375} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2 a - 3\) , \( -19\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a-3\right){x}-19$
27075.2-a2 27075.2-a \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.190825450$ $0.979532675$ 2.590036220 \( \frac{90458382169}{2671875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -93 a + 92\) , \( -285\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-93a+92\right){x}-285$
27075.2-b1 27075.2-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.885163107$ 1.533147475 \( \frac{1256216039}{15582375} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 23 a - 24\) , \( -199\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(23a-24\right){x}-199$
27075.2-b2 27075.2-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.221290776$ 1.533147475 \( \frac{209595169258201}{41748046875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1237 a + 1236\) , \( 14291\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1237a+1236\right){x}+14291$
27075.2-b3 27075.2-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.442581553$ 1.533147475 \( \frac{6189976379881}{456890625} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -382 a + 381\) , \( -2467\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-382a+381\right){x}-2467$
27075.2-b4 27075.2-b \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.221290776$ 1.533147475 \( \frac{23977812996389881}{146611125} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -6007 a + 6006\) , \( -175717\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-6007a+6006\right){x}-175717$
27075.2-c1 27075.2-c \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.067413588$ $1.577532480$ 2.455981678 \( \frac{756058031}{438615} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -19 a\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}-19a{x}$
27075.2-c2 27075.2-c \(\Q(\sqrt{-3}) \) \( 3 \cdot 5^{2} \cdot 19^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.134827177$ $0.788766240$ 2.455981678 \( \frac{48587168449}{28048275} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 76 a\) , \( -19\bigr] \) ${y}^2+a{x}{y}={x}^{3}+76a{x}-19$
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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.