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

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

Rank

The elliptic curves in class 235200d 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 6 T + 23 T^{2}\)	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 235200d do not have complex multiplication.

Modular form 235200.2.a.d

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 235200d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
235200.d2	235200d1	\([0, -1, 0, -2613, 76077]\)	\(-40960/27\)	\(-1301103820800\)	\([]\)	\(435456\)	\(1.0254\)	\(\Gamma_0(N)\)-optimal
235200.d1	235200d2	\([0, -1, 0, -237813, 44717037]\)	\(-30866268160/3\)	\(-144567091200\)	\([]\)	\(1306368\)	\(1.5747\)