Elliptic curve isogeny class with Cremona label 21054bh (LMFDB label 21054.bc)

• Label: 21054bh
• Number of curves: $2$
• Conductor: $21054$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 21054bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21054bh do not have complex multiplication.

Modular form 21054.2.a.bh

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 21054bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21054.bc1	21054bh1	\([1, 0, 0, -932247, -1633393431]\)	\(-50577879066661513/621261297432576\)	\(-1100602285340951771136\)	\([]\)	\(1663200\)	\(2.7193\)	\(\Gamma_0(N)\)-optimal
21054.bc2	21054bh2	\([1, 0, 0, 8329698, 42347878596]\)	\(36079072622241241607/458176313589497856\)	\(-811687288278924411273216\)	\([]\)	\(4989600\)	\(3.2686\)