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Results (4 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
525.1-e4 525.1-e \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $0.259415011$ $14.46234780$ 1.637397992 \( \frac{1771561}{105} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 12 a - 36\) , \( 42 a - 120\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-36\right){x}+42a-120$
525.1-k4 525.1-k \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \cdot 7 \) $0$ $\Z/4\Z$ $1$ $34.38008640$ 1.875587480 \( \frac{1771561}{105} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -3\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-3{x}+1$
1575.1-l4 1575.1-l \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $12.87396296$ 2.809329036 \( \frac{1771561}{105} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 7 a - 23\) , \( -15 a + 41\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-23\right){x}-15a+41$
1575.1-p4 1575.1-p \(\Q(\sqrt{21}) \) \( 3^{2} \cdot 5^{2} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $12.87396296$ 2.809329036 \( \frac{1771561}{105} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -8 a - 15\) , \( 15 a + 26\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-8a-15\right){x}+15a+26$
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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.