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-a3	75.1-a	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{4} \cdot 5^{16} \)	$1.98537$	$(4a+13), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{5} \)	$1$	$2.547989231$	2.699915346	\( \frac{4733169839}{3515625} \)	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 422549 a + 1383816\) , \( 155447492 a + 509077665\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(422549a+1383816\right){x}+155447492a+509077665$
75.1-b3	75.1-b	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( 3^{4} \cdot 5^{16} \)	$1.98537$	$(4a+13), (5)$	$1$	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{4} \)	$8.222150098$	$1.961688882$	1.068189016	\( \frac{4733169839}{3515625} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
225.1-a3	225.1-a	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	225.1	\( 3^{2} \cdot 5^{2} \)	\( 3^{10} \cdot 5^{16} \)	$2.61289$	$(4a+13), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$8.055414916$	$1.290782985$	2.754442525	\( \frac{4733169839}{3515625} \)	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 4197 a + 13752\) , \( -157371 a - 515373\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4197a+13752\right){x}-157371a-515373$
225.1-b3	225.1-b	$8$	$16$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	225.1	\( 3^{2} \cdot 5^{2} \)	\( 3^{10} \cdot 5^{16} \)	$2.61289$	$(4a+13), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$8.055414916$	$1.290782985$	2.754442525	\( \frac{4733169839}{3515625} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( -4197 a + 17949\) , \( 157371 a - 672744\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-4197a+17949\right){x}+157371a-672744$

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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.