Elliptic curve isogeny class with LMFDB label 214200.et (Cremona label 214200bj)

• Label: 214200.et
• Number of curves: $4$
• Conductor: $214200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 214200.et have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 214200.et do not have complex multiplication.

Modular form 214200.2.a.et

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 214200.et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
214200.et1	214200bj4	\([0, 0, 0, -176421675, -901936584250]\)	\(26031669916232627138/1534698375\)	\(35801443692000000000\)	\([2]\)	\(21233664\)	\(3.2163\)
214200.et2	214200bj3	\([0, 0, 0, -18543675, 7425701750]\)	\(30229685362358498/16472900390625\)	\(384279820312500000000000\)	\([2]\)	\(21233664\)	\(3.2163\)
214200.et3	214200bj2	\([0, 0, 0, -11046675, -14038209250]\)	\(12781179439594276/97578140625\)	\(1138151432250000000000\)	\([2, 2]\)	\(10616832\)	\(2.8697\)
214200.et4	214200bj1	\([0, 0, 0, -242175, -500170750]\)	\(-538671647824/36750606375\)	\(-107164768189500000000\)	\([4]\)	\(5308416\)	\(2.5232\)	\(\Gamma_0(N)\)-optimal