Elliptic curve isogeny class with Cremona label 229840j (LMFDB label 229840.ba)

• Label: 229840j
• Number of curves: $2$
• Conductor: $229840$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 229840j have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 229840j do not have complex multiplication.

Modular form 229840.2.a.j

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 229840j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
229840.ba1	229840j1	\([0, 0, 0, -4732, -125229]\)	\(151732224/85\)	\(6564460240\)	\([2]\)	\(184320\)	\(0.83093\)	\(\Gamma_0(N)\)-optimal
229840.ba2	229840j2	\([0, 0, 0, -3887, -171366]\)	\(-5256144/7225\)	\(-8927665926400\)	\([2]\)	\(368640\)	\(1.1775\)