Elliptic curve isogeny class with Cremona label 145040g (LMFDB label 145040.k)

• Label: 145040g
• Number of curves: $4$
• Conductor: $145040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 145040g have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145040g do not have complex multiplication.

Modular form 145040.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 145040g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145040.k3	145040g1	\([0, 1, 0, -58816, -3021516]\)	\(46694890801/18944000\)	\(9128929918976000\)	\([2]\)	\(829440\)	\(1.7603\)	\(\Gamma_0(N)\)-optimal
145040.k4	145040g2	\([0, 1, 0, 192064, -21787340]\)	\(1625964918479/1369000000\)	\(-659707826176000000\)	\([2]\)	\(1658880\)	\(2.1069\)
145040.k1	145040g3	\([0, 1, 0, -4135616, -3238495436]\)	\(16232905099479601/4052240\)	\(1952735165480960\)	\([2]\)	\(2488320\)	\(2.3096\)
145040.k2	145040g4	\([0, 1, 0, -4119936, -3264254540]\)	\(-16048965315233521/256572640900\)	\(-123639867921383833600\)	\([2]\)	\(4976640\)	\(2.6562\)