Elliptic curves over \(\Q(\sqrt{-10}) \) of conductor 121.2

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 40

Note: The completeness Only modular elliptic curves are included

Results (6 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
121.2-a1	121.2-a	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 11^{2} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.1	$1$	\( 1 \)	$6.056438525$	$0.370308724$	1.418440926	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \)	${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$
121.2-a2	121.2-a	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 11^{10} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.1	$1$	\( 5^{2} \)	$1.211287705$	$1.851543623$	1.418440926	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \)	${y}^2+{y}={x}^3-{x}^2-10{x}-20$
121.2-a3	121.2-a	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 11^{2} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.1	$1$	\( 1 \)	$6.056438525$	$9.257718117$	1.418440926	\( -\frac{4096}{11} \)	\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{y}={x}^3-{x}^2$
121.2-b1	121.2-b	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 2^{12} \cdot 11^{2} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.3	$25$	\( 1 \)	$0.915095465$	$0.370308724$	5.357970920	\( -\frac{52893159101157376}{11} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -31281\) , \( 2139919\bigr] \)	${y}^2={x}^3-{x}^2-31281{x}+2139919$
121.2-b2	121.2-b	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 2^{12} \cdot 11^{10} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.3	$1$	\( 5^{2} \)	$0.183019093$	$1.851543623$	5.357970920	\( -\frac{122023936}{161051} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 199\bigr] \)	${y}^2={x}^3-{x}^2-41{x}+199$
121.2-b3	121.2-b	$3$	$25$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	121.2	\( 11^{2} \)	\( 2^{12} \cdot 11^{2} \)	$1.87441$	$(a+1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5Cs.1.3	$1$	\( 1 \)	$0.915095465$	$9.257718117$	5.357970920	\( -\frac{4096}{11} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -1\bigr] \)	${y}^2={x}^3-{x}^2-{x}-1$

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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.