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
121.1-b2	121.1-b	$3$	$25$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{10} \)	$1.35814$	$(11)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.1	$1$	\( 5 \)	$13.20202978$	$1.610892258$	1.856340101	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)	${y}^2+{y}={x}^{3}-{x}^{2}-10{x}-20$
121.1-c2	121.1-c	$3$	$25$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	121.1	\( 11^{2} \)	\( 11^{10} \)	$1.35814$	$(11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.4.1	$1$	\( 5 \)	$0.111136147$	$8.512583687$	2.064462905	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( 52 a - 143\) , \( -525 a + 1465\bigr] \)	${y}^2+{y}={x}^{3}-a{x}^{2}+\left(52a-143\right){x}-525a+1465$
1089.1-c2	1089.1-c	$3$	$25$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{10} \)	$2.35237$	$(-a+2), (11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$5$	5Cs.4.1	$1$	\( 1 \)	$4.218562309$	$2.137978418$	3.936299486	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -30 a - 60\) , \( -237 a - 415\bigr] \)	${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-60\right){x}-237a-415$
1089.1-d2	1089.1-d	$3$	$25$	\(\Q(\sqrt{21}) \)	$2$	$[2, 0]$	1089.1	\( 3^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 11^{10} \)	$2.35237$	$(-a+2), (11)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$5$	5Cs.4.1	$1$	\( 1 \)	$4.218562309$	$2.137978418$	3.936299486	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 32 a - 91\) , \( 268 a - 743\bigr] \)	${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(32a-91\right){x}+268a-743$

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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.