Elliptic curve isogeny class with Cremona label 131904bw (LMFDB label 131904.be)

• Label: 131904bw
• Number of curves: $2$
• Conductor: $131904$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 131904bw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(229\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 131904bw do not have complex multiplication.

Modular form 131904.2.a.bw

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 131904bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
131904.be2	131904bw1	\([0, 0, 0, 5940, 112752]\)	\(4492125/3664\)	\(-18905435209728\)	\([2]\)	\(175104\)	\(1.2353\)	\(\Gamma_0(N)\)-optimal
131904.be1	131904bw2	\([0, 0, 0, -28620, 983664]\)	\(502459875/209764\)	\(1082336165756928\)	\([2]\)	\(350208\)	\(1.5819\)