Elliptic curve isogeny class with LMFDB label 217854.dz (Cremona label 217854bg)

• Label: 217854.dz
• Number of curves: $4$
• Conductor: $217854$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 217854.dz have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 217854.dz do not have complex multiplication.

Modular form 217854.2.a.dz

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 217854.dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
217854.dz1	217854bg3	\([1, -1, 1, -90929, 10566091]\)	\(969417177273/1085318\)	\(93083514911478\)	\([2]\)	\(1253376\)	\(1.5945\)
217854.dz2	217854bg4	\([1, -1, 1, -64469, -6230717]\)	\(345505073913/3388346\)	\(290605293025866\)	\([2]\)	\(1253376\)	\(1.5945\)
217854.dz3	217854bg2	\([1, -1, 1, -7139, 75583]\)	\(469097433/244036\)	\(20930021104356\)	\([2, 2]\)	\(626688\)	\(1.2479\)
217854.dz4	217854bg1	\([1, -1, 1, 1681, 8551]\)	\(6128487/3952\)	\(-338947710192\)	\([2]\)	\(313344\)	\(0.90134\)	\(\Gamma_0(N)\)-optimal