Elliptic curve search results

Results (4 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
75.1-a7	75.1-a	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{2} \cdot 5^{2} \)	$1.98537$	$(4a+13), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$16$	\( 2 \)	$1$	$2.547989231$	2.699915346	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -966651 a - 3165699\) , \( -1006909063 a - 3297543830\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-966651a-3165699\right){x}-1006909063a-3297543830$
75.1-b7	75.1-b	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{2} \cdot 5^{2} \)	$1.98537$	$(4a+13), (5)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2 \)	$1.027768762$	$31.38702211$	1.068189016	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
225.1-a7	225.1-a	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	225.1	\( 3^{2} \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \)	$2.61289$	$(4a+13), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$4.027707458$	$5.163131942$	2.754442525	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -9603 a - 31443\) , \( 1004859 a + 3290832\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9603a-31443\right){x}+1004859a+3290832$
225.1-b7	225.1-b	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	225.1	\( 3^{2} \cdot 5^{2} \)	\( 3^{8} \cdot 5^{2} \)	$2.61289$	$(4a+13), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2 \)	$4.027707458$	$5.163131942$	2.754442525	\( \frac{56667352321}{15} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( 9603 a - 41046\) , \( -1004859 a + 4295691\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(9603a-41046\right){x}-1004859a+4295691$

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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.