Elliptic curve isogeny class with Cremona label 235200bby (LMFDB label 235200.bby)

• Label: 235200bby
• Number of curves: $2$
• Conductor: $235200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 235200bby have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 235200bby do not have complex multiplication.

Modular form 235200.2.a.bby

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 235200bby

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.bby2	235200bby1	\([0, 1, 0, -80033, -20123937]\)	\(-2401/6\)	\(-141675749376000000\)	\([]\)	\(2257920\)	\(1.9789\)	\(\Gamma_0(N)\)-optimal
235200.bby1	235200bby2	\([0, 1, 0, -11056033, 14676740063]\)	\(-6329617441/279936\)	\(-6610023762886656000000\)	\([]\)	\(15805440\)	\(2.9519\)