Elliptic curve isogeny class with LMFDB label 203840.cb (Cremona label 203840w)

• Label: 203840.cb
• Number of curves: $3$
• Conductor: $203840$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 203840.cb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 9 T + 23 T^{2}\)	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 203840.cb do not have complex multiplication.

Modular form 203840.2.a.cb

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 203840.cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
203840.cb1	203840w3	\([0, -1, 0, -158378027425, -25728325474706623]\)	\(-14245586655234650511684983641/1028175397808386133196800\)	\(-31709936320973064158437788404940800\)	\([]\)	\(1755758592\)	\(5.3698\)
203840.cb2	203840w1	\([0, -1, 0, -1814011425, 32246069962177]\)	\(-21405018343206000779641/2177246093750000000\)	\(-67148402048000000000000000000\)	\([]\)	\(195084288\)	\(4.2712\)	\(\Gamma_0(N)\)-optimal
203840.cb3	203840w2	\([0, -1, 0, 11170988575, -29580807037823]\)	\(4998853083179567995470359/2905108466204672000000\)	\(-89596390523669959443218432000000\)	\([]\)	\(585252864\)	\(4.8205\)