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Results (8 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
2.2-b1 2.2-b \(\Q(\sqrt{209}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.51817441$ 2.561857817 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 166348 a - 1285588\) , \( 101485499 a - 784322149\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(166348a-1285588\right){x}+101485499a-784322149$
2.2-c1 2.2-c \(\Q(\sqrt{209}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.529462610$ $13.03498084$ 1.909556628 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -1476 a - 9940\) , \( -95638 a - 643494\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1476a-9940\right){x}-95638a-643494$
50.3-a1 50.3-a \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.129561378$ $8.281579361$ 2.375010653 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
50.3-g1 50.3-g \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.786022418$ $5.829420649$ 11.52282962 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( a\) , \( 1\) , \( 557954489 a - 4312104315\) , \( -19506746796820 a + 150756256928227\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(557954489a-4312104315\right){x}-19506746796820a+150756256928227$
50.4-b1 50.4-b \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $7.111946551$ $8.281579361$ 16.29628084 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( a\) , \( 1\) , \( -4988005 a - 33561363\) , \( 16267292978 a + 109453116751\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-4988005a-33561363\right){x}+16267292978a+109453116751$
50.4-k1 50.4-k \(\Q(\sqrt{209}) \) \( 2 \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.829420649$ 0.806458915 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 1241 a - 9560\) , \( -60361 a + 466576\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(1241a-9560\right){x}-60361a+466576$
64.6-c1 64.6-c \(\Q(\sqrt{209}) \) \( 2^{6} \) $0 \le r \le 1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.288073535$ 7.117173427 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -50 a - 326\) , \( -388 a - 2613\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-50a-326\right){x}-388a-2613$
64.6-g1 64.6-g \(\Q(\sqrt{209}) \) \( 2^{6} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.271303162$ $23.42490957$ 1.758407907 \( -\frac{2361203}{4} a - 4047179 \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 310246949 a - 2397717530\) , \( -8088584565218 a + 62511947563426\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(310246949a-2397717530\right){x}-8088584565218a+62511947563426$
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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.