Elliptic curve isogeny class with Cremona label 21294ca (LMFDB label 21294.ce)

• Label: 21294ca
• Number of curves: $2$
• Conductor: $21294$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 21294ca have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21294ca do not have complex multiplication.

Modular form 21294.2.a.ca

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 21294ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21294.ce2	21294ca1	\([1, -1, 1, -133880, 1971155]\)	\(2640625/1512\)	\(151954246923576552\)	\([]\)	\(209664\)	\(1.9866\)	\(\Gamma_0(N)\)-optimal
21294.ce1	21294ca2	\([1, -1, 1, -7845350, 8459911451]\)	\(531373116625/2058\)	\(206826613868201418\)	\([]\)	\(628992\)	\(2.5359\)