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Results (5 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
361.2-a1 361.2-a \(\Q(\sqrt{-3}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $2.033701819$ $0.935309008$ 0.488089257 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$
361.2-a2 361.2-a \(\Q(\sqrt{-3}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $0.225966868$ $0.935309008$ 0.488089257 \( -\frac{14306161739497472}{322687697779} a - \frac{12817090105540608}{322687697779} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 31 a + 99\) , \( 498 a - 424\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(31a+99\right){x}+498a-424$
361.2-a3 361.2-a \(\Q(\sqrt{-3}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $0.225966868$ $0.935309008$ 0.488089257 \( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -99 a - 31\) , \( -498 a + 74\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-99a-31\right){x}-498a+74$
361.2-a4 361.2-a \(\Q(\sqrt{-3}) \) \( 19^{2} \) $1$ $\Z/3\Z\oplus\Z/3\Z$ $0.677900606$ $2.805927025$ 0.488089257 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( -9 a + 9\) , \( -15\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-9a+9\right){x}-15$
361.2-a5 361.2-a \(\Q(\sqrt{-3}) \) \( 19^{2} \) $1$ $\Z/3\Z$ $0.225966868$ $8.417781075$ 0.488089257 \( \frac{32768}{19} \) \( \bigl[0\) , \( -a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(a-1\right){x}$
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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.