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Results (12 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
384.1-b2 384.1-b \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $18.42598142$ 1.329780666 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 38 a - 66\) , \( -180 a + 312\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(38a-66\right){x}-180a+312$
384.1-e2 384.1-e \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.135650867$ 1.761420081 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 38 a - 66\) , \( 180 a - 312\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(38a-66\right){x}+180a-312$
768.1-b2 768.1-b \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.135650867$ 1.174280054 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 532 a - 919\) , \( 8829 a - 15293\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(532a-919\right){x}+8829a-15293$
768.1-o2 768.1-o \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.178968844$ $18.42598142$ 2.855871714 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 532 a - 919\) , \( -8829 a + 15293\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(532a-919\right){x}-8829a+15293$
1152.1-k2 1152.1-k \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.712153510$ $5.799519847$ 2.866448324 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 1594 a - 2760\) , \( 44284 a - 76702\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(1594a-2760\right){x}+44284a-76702$
1152.1-o2 1152.1-o \(\Q(\sqrt{3}) \) \( 2^{7} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.616078324$ 1.243623784 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1594 a - 2760\) , \( -44284 a + 76702\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(1594a-2760\right){x}-44284a+76702$
2304.1-k2 2304.1-k \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.799519847$ 1.674177172 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 114 a - 198\) , \( 936 a - 1620\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(114a-198\right){x}+936a-1620$
2304.1-m2 2304.1-m \(\Q(\sqrt{3}) \) \( 2^{8} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.616078324$ 2.487247569 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 114 a - 198\) , \( -936 a + 1620\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(114a-198\right){x}-936a+1620$
3072.1-a2 3072.1-a \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $7.102932189$ 3.075659858 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 284 a - 492\) , \( 3672 a - 6360\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(284a-492\right){x}+3672a-6360$
3072.1-j2 3072.1-j \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $7.102932189$ 1.025219952 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 36\) , \( 72 a - 120\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-36\right){x}+72a-120$
3072.1-bz2 3072.1-bz \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.486628419$ $10.55249773$ 4.447166274 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 36\) , \( -72 a + 120\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-36\right){x}-72a+120$
3072.1-ca2 3072.1-ca \(\Q(\sqrt{3}) \) \( 2^{10} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.985739672$ $10.55249773$ 3.002803272 \( -\frac{770336}{27} a + \frac{1419904}{27} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 284 a - 492\) , \( -3672 a + 6360\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(284a-492\right){x}-3672a+6360$
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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.