Elliptic curve isogeny class with Cremona label 213444h (LMFDB label 213444.j)

• Label: 213444h
• Number of curves: $2$
• Conductor: $213444$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 213444h have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 213444h do not have complex multiplication.

Modular form 213444.2.a.h

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 213444h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
213444.j2	213444h1	\([0, 0, 0, 142296, 23739716]\)	\(8192/11\)	\(-427862800879024896\)	\([]\)	\(2592000\)	\(2.0689\)	\(\Gamma_0(N)\)-optimal
213444.j1	213444h2	\([0, 0, 0, -4126584, 3245036564]\)	\(-199794688/1331\)	\(-51771398906362012416\)	\([]\)	\(7776000\)	\(2.6182\)