Elliptic curve isogeny class with Cremona label 204490d (LMFDB label 204490.bu)

• Label: 204490d
• Number of curves: $4$
• Conductor: $204490$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 204490d have rank \(0\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 204490.2.a.d

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 204490d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
204490.bu4	204490d1	\([1, 0, 0, 2126270, 25516932]\)	\(124326214271/71980480\)	\(-615504118419108867520\)	\([2]\)	\(15482880\)	\(2.6785\)	\(\Gamma_0(N)\)-optimal
204490.bu3	204490d2	\([1, 0, 0, -8507210, 202032700]\)	\(7962857630209/4606058600\)	\(39386345269992014551400\)	\([2]\)	\(30965760\)	\(3.0251\)
204490.bu2	204490d3	\([1, 0, 0, -29365190, 65395489600]\)	\(-327495950129089/26547449500\)	\(-227006884377171595625500\)	\([2]\)	\(46448640\)	\(3.2279\)
204490.bu1	204490d4	\([1, 0, 0, -478629720, 4030334672662]\)	\(1418098748958579169/8307406250\)	\(71036519348796300406250\)	\([2]\)	\(92897280\)	\(3.5744\)