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

• Label: 235200qu
• Number of curves: $2$
• Conductor: $235200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 235200qu have rank \(0\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 235200.2.a.qu

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 235200qu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.qu1	235200qu1	\([0, 1, 0, -206208, 35342838]\)	\(65939264/1323\)	\(19456203375000000\)	\([2]\)	\(2211840\)	\(1.9170\)	\(\Gamma_0(N)\)-optimal
235200.qu2	235200qu2	\([0, 1, 0, 8167, 105443463]\)	\(64/5103\)	\(-4802902776000000000\)	\([2]\)	\(4423680\)	\(2.2635\)