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Results (3 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
5324.6-c1 5324.6-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.036077686$ $4.305972120$ 3.288129422 \( \frac{399175}{1408} a + \frac{5454499}{1408} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a + 1\) , \( -a + 3\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+1\right){x}-a+3$
42592.18-k1 42592.18-k \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.104477125$ $0.649149721$ 8.613037707 \( \frac{399175}{1408} a + \frac{5454499}{1408} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 30 a + 115\) , \( -223 a + 363\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(30a+115\right){x}-223a+363$
42592.6-c1 42592.6-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 11^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.649149721$ 1.962844260 \( \frac{399175}{1408} a + \frac{5454499}{1408} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -54 a - 89\) , \( -250 a - 123\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-54a-89\right){x}-250a-123$
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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.