Elliptic curve isogeny class with Cremona label 217800eq (LMFDB label 217800.f)

• Label: 217800eq
• Number of curves: $4$
• Conductor: $217800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 217800eq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 217800eq do not have complex multiplication.

Modular form 217800.2.a.eq

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 217800eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
217800.f3	217800eq1	\([0, 0, 0, -92982450, 344943124625]\)	\(275361373935616/148240125\)	\(47861843289514031250000\)	\([2]\)	\(35389440\)	\(3.3010\)	\(\Gamma_0(N)\)-optimal
217800.f2	217800eq2	\([0, 0, 0, -109453575, 214310632250]\)	\(28071778927696/12404390625\)	\(64079492668605562500000000\)	\([2, 2]\)	\(70778880\)	\(3.6476\)
217800.f4	217800eq3	\([0, 0, 0, 375695925, 1596501557750]\)	\(283811208976796/217529296875\)	\(-4494913907730468750000000000\)	\([2]\)	\(141557760\)	\(3.9942\)
217800.f1	217800eq4	\([0, 0, 0, -858141075, -9528359805250]\)	\(3382175663521924/59189241375\)	\(1223056149523552278000000000\)	\([2]\)	\(141557760\)	\(3.9942\)