Elliptic curve isogeny class with Cremona label 162240fd (LMFDB label 162240.hk)

• Label: 162240fd
• Number of curves: $2$
• Conductor: $162240$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 162240fd have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162240fd do not have complex multiplication.

Modular form 162240.2.a.fd

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 162240fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162240.hk1	162240fd1	\([0, 1, 0, -1437505, -639405025]\)	\(570403428460237/23887872000\)	\(13757750911696896000\)	\([2]\)	\(4976640\)	\(2.4372\)	\(\Gamma_0(N)\)-optimal
162240.hk2	162240fd2	\([0, 1, 0, 692415, -2370178017]\)	\(63745936931123/4251528000000\)	\(-2448584085602304000000\)	\([2]\)	\(9953280\)	\(2.7837\)