Elliptic curve isogeny class with LMFDB label 5904.q (Cremona label 5904h)

• Label: 5904.q
• Number of curves: $2$
• Conductor: $5904$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 5904.q have rank \(1\).

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
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 5904.2.a.q

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 5904.q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5904.q1	5904h1	\([0, 0, 0, -99, -270]\)	\(143748/41\)	\(30606336\)	\([2]\)	\(1024\)	\(0.14302\)	\(\Gamma_0(N)\)-optimal
5904.q2	5904h2	\([0, 0, 0, 261, -1782]\)	\(1317006/1681\)	\(-2509719552\)	\([2]\)	\(2048\)	\(0.48959\)