Elliptic curve isogeny class with Cremona label 21632m (LMFDB label 21632.be)

• Label: 21632m
• Number of curves: $2$
• Conductor: $21632$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 21632m have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21632m do not have complex multiplication.

Modular form 21632.2.a.m

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 21632m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21632.be1	21632m1	\([0, -1, 0, -394, 2898]\)	\(10976\)	\(617831552\)	\([2]\)	\(9216\)	\(0.42604\)	\(\Gamma_0(N)\)-optimal
21632.be2	21632m2	\([0, -1, 0, 451, 12869]\)	\(128\)	\(-79082438656\)	\([2]\)	\(18432\)	\(0.77262\)