Elliptic curve isogeny class with LMFDB label 207552.bl (Cremona label 207552bl)

• Label: 207552.bl
• Number of curves: $4$
• Conductor: $207552$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 207552.bl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(23\)	\(1 + T\)
\(47\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 207552.bl do not have complex multiplication.

Modular form 207552.2.a.bl

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 207552.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
207552.bl1	207552bl4	\([0, 1, 0, -11695809, -15399389025]\)	\(674954705500996959793/9588192183\)	\(2513487051620352\)	\([2]\)	\(5799936\)	\(2.5086\)
207552.bl2	207552bl3	\([0, 1, 0, -1077569, 9758751]\)	\(527860858731041233/305306328935961\)	\(80034222292588560384\)	\([2]\)	\(5799936\)	\(2.5086\)
207552.bl3	207552bl2	\([0, 1, 0, -731649, -240341409]\)	\(165231457514151553/621021226401\)	\(162796988373663744\)	\([2, 2]\)	\(2899968\)	\(2.1620\)
207552.bl4	207552bl1	\([0, 1, 0, -24769, -7212385]\)	\(-6411014266033/81817611327\)	\(-21447995903705088\)	\([2]\)	\(1449984\)	\(1.8154\)	\(\Gamma_0(N)\)-optimal