Elliptic curve isogeny class with Cremona label 154800en (LMFDB label 154800.gg)

• Label: 154800en
• Number of curves: $2$
• Conductor: $154800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 154800en have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.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 154800en do not have complex multiplication.

Modular form 154800.2.a.en

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.

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

Isogeny graph

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

Elliptic curves in class 154800en

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
154800.gg2	154800en1	\([0, 0, 0, -31251075, 67234957250]\)	\(1953326569433829507/262451171875\)	\(453515625000000000000\)	\([2]\)	\(13762560\)	\(2.9825\)	\(\Gamma_0(N)\)-optimal
154800.gg1	154800en2	\([0, 0, 0, -500001075, 4303328707250]\)	\(8000051600110940079507/144453125\)	\(249615000000000000\)	\([2]\)	\(27525120\)	\(3.3291\)