Elliptic curve isogeny class with Cremona label 272322h (LMFDB label 272322.h)

• Label: 272322h
• Number of curves: $4$
• Conductor: $272322$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 272322h have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 272322h do not have complex multiplication.

Modular form 272322.2.a.h

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 272322h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
272322.h4	272322h1	\([1, -1, 0, 4728, -20566]\)	\(3375/2\)	\(-6925651983378\)	\([]\)	\(403920\)	\(1.1532\)	\(\Gamma_0(N)\)-optimal
272322.h3	272322h2	\([1, -1, 0, -70917, -7600195]\)	\(-140625/8\)	\(-2243911242614472\)	\([]\)	\(1211760\)	\(1.7025\)
272322.h1	272322h3	\([1, -1, 0, -1810752, 938310272]\)	\(-189613868625/128\)	\(-443241726936192\)	\([]\)	\(2827440\)	\(2.1262\)
272322.h2	272322h4	\([1, -1, 0, -1432527, 1340938349]\)	\(-1159088625/2097152\)	\(-588227868783928147968\)	\([]\)	\(8482320\)	\(2.6755\)