Elliptic curve search results

Results (3 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
15.1-a5	15.1-a	$6$	$8$	4.4.9301.1	$4$	$[4, 0]$	15.1	\( 3 \cdot 5 \)	\( - 3^{3} \cdot 5^{3} \)	$12.08968$	$(-a), (-a^3+a^2+4a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3Ns	$1$	\( 3 \)	$0.213181193$	$1431.058592$	2.372481019	\( -\frac{6637246}{3375} a^{3} + \frac{11349478}{3375} a^{2} + \frac{20884829}{3375} a - \frac{16775914}{3375} \)	\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} + 5 a + 5\) , \( 2 a^{2} + 4 a + 1\bigr] \)	${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(a^{2}+5a+5\right){x}+2a^{2}+4a+1$
45.1-a3	45.1-a	$6$	$8$	4.4.9301.1	$4$	$[4, 0]$	45.1	\( 3^{2} \cdot 5 \)	\( - 3^{9} \cdot 5^{3} \)	$13.86931$	$(-a), (-a^3+a^2+4a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Ns	$1$	\( 2 \)	$0.566171963$	$290.8000537$	3.414349822	\( -\frac{6637246}{3375} a^{3} + \frac{11349478}{3375} a^{2} + \frac{20884829}{3375} a - \frac{16775914}{3375} \)	\( \bigl[a^{2} - a - 3\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - 4 a - 3\) , \( a^{3} - 4 a - 6\) , \( -a^{3} + 4 a^{2} - a - 10\bigr] \)	${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(a^{3}-4a-6\right){x}-a^{3}+4a^{2}-a-10$
75.1-a5	75.1-a	$6$	$8$	4.4.9301.1	$4$	$[4, 0]$	75.1	\( 3 \cdot 5^{2} \)	\( - 3^{3} \cdot 5^{9} \)	$14.78380$	$(-a), (-a^3+a^2+4a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3Ns	$1$	\( 2 \cdot 3 \)	$0.254610494$	$292.8993696$	4.639606677	\( -\frac{6637246}{3375} a^{3} + \frac{11349478}{3375} a^{2} + \frac{20884829}{3375} a - \frac{16775914}{3375} \)	\( \bigl[a\) , \( a^{2} - a - 2\) , \( 0\) , \( -10 a^{3} + 2 a^{2} + 51 a + 34\) , \( 0\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-10a^{3}+2a^{2}+51a+34\right){x}$

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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.