Elliptic curves over \(\Q(\sqrt{-35}) \) of conductor 35.1

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 35

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
35.1-a1	35.1-a	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 3^{12} \cdot 5^{18} \cdot 7^{2} \)	$1.28585$	$(5,a+2), (7,a+3)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs	$1$	\( 2^{2} \cdot 3^{2} \)	$0.034009387$	$0.774975202$	1.283054450	\( -\frac{250523582464}{13671875} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 131 a + 1048\) , \( 5198 a - 11046\bigr] \)	${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(131a+1048\right){x}+5198a-11046$
35.1-a2	35.1-a	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 3^{12} \cdot 5^{2} \cdot 7^{2} \)	$1.28585$	$(5,a+2), (7,a+3)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs	$1$	\( 2^{2} \)	$0.034009387$	$6.974776820$	1.283054450	\( -\frac{262144}{35} \)	\( \bigl[0\) , \( -a\) , \( 1\) , \( -a + 9\) , \( 2 a + 2\bigr] \)	${y}^2+{y}={x}^3-a{x}^2+\left(-a+9\right){x}+2a+2$
35.1-a3	35.1-a	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 3^{12} \cdot 5^{6} \cdot 7^{6} \)	$1.28585$	$(5,a+2), (7,a+3)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs	$1$	\( 2^{2} \cdot 3 \)	$0.034009387$	$2.324925606$	1.283054450	\( \frac{71991296}{42875} \)	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -9 a - 72\) , \( -10 a + 21\bigr] \)	${y}^2+{y}={x}^3+\left(a-1\right){x}^2+\left(-9a-72\right){x}-10a+21$
35.1-b1	35.1-b	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 5^{18} \cdot 7^{2} \)	$1.28585$	$(5,a+2), (7,a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs.1.1	$1$	\( 2^{2} \)	$1$	$0.774975202$	1.047957743	\( -\frac{250523582464}{13671875} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \)	${y}^2+{y}={x}^3+{x}^2-131{x}-650$
35.1-b2	35.1-b	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 5^{2} \cdot 7^{2} \)	$1.28585$	$(5,a+2), (7,a+3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs.1.1	$1$	\( 2^{2} \)	$1$	$6.974776820$	1.047957743	\( -\frac{262144}{35} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -1\) , \( 0\bigr] \)	${y}^2+{y}={x}^3+{x}^2-{x}$
35.1-b3	35.1-b	$3$	$9$	\(\Q(\sqrt{-35}) \)	$2$	$[0, 1]$	35.1	\( 5 \cdot 7 \)	\( 5^{6} \cdot 7^{6} \)	$1.28585$	$(5,a+2), (7,a+3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cn, 3Cs.1.1	$1$	\( 2^{2} \cdot 3 \)	$1$	$2.324925606$	1.047957743	\( \frac{71991296}{42875} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( 9\) , \( 1\bigr] \)	${y}^2+{y}={x}^3+{x}^2+9{x}+1$

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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.