Elliptic curve isogeny class with Cremona label 21850c (LMFDB label 21850.a)

• Label: 21850c
• Number of curves: $2$
• Conductor: $21850$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 21850c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(19\)	\(1 + T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21850c do not have complex multiplication.

Modular form 21850.2.a.c

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 21850c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21850.a2	21850c1	\([1, 1, 0, -198225, -33792875]\)	\(55129288688387857/484804919296\)	\(7575076864000000\)	\([]\)	\(145152\)	\(1.8706\)	\(\Gamma_0(N)\)-optimal
21850.a1	21850c2	\([1, 1, 0, -16022225, -24691632875]\)	\(29112011033527546515217/20192896\)	\(315514000000\)	\([]\)	\(435456\)	\(2.4199\)