Elliptic curve isogeny class with Cremona label 5904r (LMFDB label 5904.n)

• Label: 5904r
• Number of curves: $2$
• Conductor: $5904$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 5904r have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5904r do not have complex multiplication.

Modular form 5904.2.a.r

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 5904r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5904.n1	5904r1	\([0, 0, 0, -9579, 358810]\)	\(32553430057/212544\)	\(634652983296\)	\([2]\)	\(9216\)	\(1.1006\)	\(\Gamma_0(N)\)-optimal
5904.n2	5904r2	\([0, 0, 0, -3819, 786202]\)	\(-2062933417/88232328\)	\(-263460319690752\)	\([2]\)	\(18432\)	\(1.4472\)