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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3872.14-d1 3872.14-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/4\Z$ $1$ $0.478347664$ 2.892774765 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 30 a + 86\) , \( -500 a - 580\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(30a+86\right){x}-500a-580$
3872.5-d1 3872.5-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.478347664$ 2.892774765 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -48 a - 65\) , \( 352 a - 1185\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-48a-65\right){x}+352a-1185$
5324.6-d1 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/4\Z$ $0.245619348$ $0.288454494$ 3.427684460 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -48 a - 272\) , \( -3251 a + 4009\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-272\right){x}-3251a+4009$
5324.7-c1 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $1.964954788$ $0.288454494$ 3.427684460 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 157 a + 140\) , \( 3795 a - 654\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(157a+140\right){x}+3795a-654$
15488.20-c2 15488.20-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -148 a - 29\) , \( -567 a - 2768\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-148a-29\right){x}-567a-2768$
15488.5-c2 15488.5-c \(\Q(\sqrt{-7}) \) \( 2^{7} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.338242877$ 1.022750326 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 228\) , \( -129 a - 3075\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+228\right){x}-129a-3075$
23716.5-e2 23716.5-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7^{2} \cdot 11^{2} \) $0$ $\Z/2\Z$ $1$ $0.361596845$ 1.093366089 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 128 a - 155\) , \( 293 a + 2482\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(128a-155\right){x}+293a+2482$
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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.