Elliptic curve isogeny class with Cremona label 205504cm (LMFDB label 205504.cg)

• Label: 205504cm
• Number of curves: $2$
• Conductor: $205504$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 205504cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 205504cm do not have complex multiplication.

Modular form 205504.2.a.cm

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 205504cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
205504.cg2	205504cm1	\([0, -1, 0, 191, -2367]\)	\(5324/19\)	\(-2735669248\)	\([2]\)	\(90624\)	\(0.49374\)	\(\Gamma_0(N)\)-optimal
205504.cg1	205504cm2	\([0, -1, 0, -1889, -26911]\)	\(2590058/361\)	\(103955431424\)	\([2]\)	\(181248\)	\(0.84032\)