Elliptic curve isogeny class with Cremona label 45662r (LMFDB label 45662.m)

• Label: 45662r
• Number of curves: $2$
• Conductor: $45662$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 45662r have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(17\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 45662r do not have complex multiplication.

Modular form 45662.2.a.r

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 45662r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45662.m2	45662r1	\([1, 0, 0, 283, 3805]\)	\(103823/316\)	\(-7627471804\)	\([2]\)	\(30720\)	\(0.57957\)	\(\Gamma_0(N)\)-optimal
45662.m1	45662r2	\([1, 0, 0, -2607, 43687]\)	\(81182737/12482\)	\(301285136258\)	\([2]\)	\(61440\)	\(0.92614\)