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
15.1-a5	15.1-a	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{4} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{4} \)	$1$	$31.38702211$	2.865230004	\( \frac{13997521}{225} \)	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -224 a - 1188\) , \( 3752 a + 20593\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-224a-1188\right){x}+3752a+20593$
15.1-b5	15.1-b	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$4$	\( 2^{2} \)	$1$	$10.19195692$	0.930394118	\( \frac{13997521}{225} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 425923 a - 2332891\) , \( 350864730 a - 1921765280\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(425923a-2332891\right){x}+350864730a-1921765280$
15.1-c5	15.1-c	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 2^{12} \cdot 3^{4} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$4.297783744$	$10.19195692$	3.998632720	\( \frac{13997521}{225} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 878 a - 4806\) , \( 37104 a - 203226\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(878a-4806\right){x}+37104a-203226$
15.1-d5	15.1-d	$8$	$16$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	15.1	\( 3 \cdot 5 \)	\( 3^{4} \cdot 5^{4} \)	$1.92642$	$(3,a), (a+5)$	$1$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$2.518449529$	$31.38702211$	1.803984289	\( \frac{13997521}{225} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$

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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.