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
20.1-a9	20.1-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	20.1	\( 2^{2} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$1.79105$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$224.9714518$	0.770522476	\( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \)	\( \bigl[a^{2} - 1\) , \( a^{2} - 3\) , \( 0\) , \( -625 a^{2} - 730 a + 290\) , \( -9146 a^{2} - 10702 a + 4214\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-625a^{2}-730a+290\right){x}-9146a^{2}-10702a+4214$
80.1-b1	80.1-b	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	80.1	\( 2^{4} \cdot 5 \)	\( 2^{8} \cdot 5^{2} \)	$2.25658$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{2} \)	$1$	$226.7568548$	1.164956165	\( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \)	\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 2\) , \( 0\) , \( -4591 a^{2} - 5372 a + 2118\) , \( 152788 a^{2} + 178776 a - 70406\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(-4591a^{2}-5372a+2118\right){x}+152788a^{2}+178776a-70406$
100.2-a11	100.2-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{8} \)	$2.34209$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{2} \)	$1$	$56.73514216$	1.165899989	\( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \)	\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -6979 a^{2} - 8164 a + 3220\) , \( -314976 a^{2} - 368548 a + 145146\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-6979a^{2}-8164a+3220\right){x}-314976a^{2}-368548a+145146$
400.2-e1	400.2-e	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{8} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2Cs, 3B	$1$	\( 2^{3} \)	$0.259152197$	$75.70894508$	2.419148294	\( -\frac{108768}{25} a^{2} + \frac{75424}{25} a + \frac{407296}{25} \)	\( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - 1\) , \( -51231 a^{2} - 59948 a + 23609\) , \( 5934968 a^{2} + 6944424 a - 2734899\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-51231a^{2}-59948a+23609\right){x}+5934968a^{2}+6944424a-2734899$

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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.