Elliptic curve isogeny class with Cremona label 353925bx (LMFDB label 353925.bx)

• Label: 353925bx
• Number of curves: $2$
• Conductor: $353925$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 353925bx have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 353925bx do not have complex multiplication.

Modular form 353925.2.a.bx

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 353925bx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
353925.bx2	353925bx1	\([0, 0, 1, 36300, 3452281]\)	\(7077888/10985\)	\(-8209939606171875\)	\([]\)	\(1555200\)	\(1.7390\)	\(\Gamma_0(N)\)-optimal
353925.bx1	353925bx2	\([0, 0, 1, -1143450, 472796156]\)	\(-303464448/1625\)	\(-885361830310546875\)	\([]\)	\(4665600\)	\(2.2883\)