Elliptic curve isogeny class with Cremona label 45080u (LMFDB label 45080.bb)

• Label: 45080u
• Number of curves: $2$
• Conductor: $45080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 45080u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 45080u do not have complex multiplication.

Modular form 45080.2.a.u

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 45080u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45080.bb1	45080u1	\([0, -1, 0, -1976, -3940]\)	\(7086244/4025\)	\(484902118400\)	\([2]\)	\(49152\)	\(0.93216\)	\(\Gamma_0(N)\)-optimal
45080.bb2	45080u2	\([0, -1, 0, 7824, -39220]\)	\(219804478/129605\)	\(-31227696424960\)	\([2]\)	\(98304\)	\(1.2787\)