Elliptic curve isogeny class with LMFDB label 204490.cm (Cremona label 204490ba)

• Label: 204490.cm
• Number of curves: $2$
• Conductor: $204490$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 204490.cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 204490.cm do not have complex multiplication.

Modular form 204490.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 204490.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
204490.cm1	204490ba2	\([1, -1, 1, -1573073833, 25958346058857]\)	\(-1762712152495281/171798691840\)	\(-41957488730147620535412981760\)	\([]\)	\(206388000\)	\(4.2332\)
204490.cm2	204490ba1	\([1, -1, 1, -17927383, -47607730673]\)	\(-2609064081/2500000\)	\(-610561819196265722500000\)	\([]\)	\(29484000\)	\(3.2603\)	\(\Gamma_0(N)\)-optimal