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Results (14 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
3136.2-a1 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z$ $-32$ $N(\mathrm{U}(1))$ $0.434172091$ $9.592728448$ 2.945025478 \( -18473000 a + 26125000 \) \( \bigl[a\) , \( -1\) , \( a\) , \( 10 a - 3\) , \( -25 a - 8\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(10a-3\right){x}-25a-8$
3136.2-a2 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z$ $-32$ $N(\mathrm{U}(1))$ $0.868344182$ $4.796364224$ 2.945025478 \( -18473000 a + 26125000 \) \( \bigl[a\) , \( 0\) , \( a\) , \( 10 a - 3\) , \( 25 a + 7\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(10a-3\right){x}+25a+7$
3136.2-a3 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.868344182$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -10 a - 18\) , \( -20 a - 24\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-10a-18\right){x}-20a-24$
3136.2-a4 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-8$ $N(\mathrm{U}(1))$ $0.434172091$ $9.592728448$ 2.945025478 \( 8000 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a - 18\) , \( 20 a + 24\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-10a-18\right){x}+20a+24$
3136.2-a5 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z$ $-32$ $N(\mathrm{U}(1))$ $0.868344182$ $9.592728448$ 2.945025478 \( 18473000 a + 26125000 \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -21 a + 26\) , \( 115 a - 160\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-21a+26\right){x}+115a-160$
3136.2-a6 3136.2-a \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) $1$ $\Z/2\Z$ $-32$ $N(\mathrm{U}(1))$ $1.736688365$ $4.796364224$ 2.945025478 \( 18473000 a + 26125000 \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -19 a + 25\) , \( -135 a + 185\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a+25\right){x}-135a+185$
3136.2-b1 3136.2-b \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.142705457$ 1.464667560 \( -\frac{8738600}{2401} a + \frac{16398328}{2401} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 34 a + 46\) , \( -29 a - 45\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(34a+46\right){x}-29a-45$
3136.2-b2 3136.2-b \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.285410914$ 1.464667560 \( -\frac{65280}{49} a + \frac{179264}{49} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -32 a - 48\) , \( -48 a - 66\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-32a-48\right){x}-48a-66$
3136.2-b3 3136.2-b \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $16.57082182$ 1.464667560 \( -\frac{55566312}{7} a + \frac{79770920}{7} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -81 a - 125\) , \( 523 a + 746\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-81a-125\right){x}+523a+746$
3136.2-b4 3136.2-b \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.142705457$ 1.464667560 \( \frac{1233152}{7} a + \frac{1746880}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -20 a + 20\) , \( -92 a + 122\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a+20\right){x}-92a+122$
3136.2-c1 3136.2-c \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.418299503$ 2.269211551 \( -\frac{8738600}{2401} a + \frac{16398328}{2401} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 34 a + 46\) , \( 29 a + 45\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(34a+46\right){x}+29a+45$
3136.2-c2 3136.2-c \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.418299503$ 2.269211551 \( -\frac{65280}{49} a + \frac{179264}{49} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -32 a - 48\) , \( 48 a + 66\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-32a-48\right){x}+48a+66$
3136.2-c3 3136.2-c \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.209149751$ 2.269211551 \( -\frac{55566312}{7} a + \frac{79770920}{7} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -81 a - 125\) , \( -523 a - 747\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-81a-125\right){x}-523a-747$
3136.2-c4 3136.2-c \(\Q(\sqrt{2}) \) \( 2^{6} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.418299503$ 2.269211551 \( \frac{1233152}{7} a + \frac{1746880}{7} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a + 20\) , \( 92 a - 122\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a+20\right){x}+92a-122$
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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.