Elliptic curve isogeny class with Cremona label 172062e (LMFDB label 172062.bf)

• Label: 172062e
• Number of curves: $2$
• Conductor: $172062$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 172062e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 172062e do not have complex multiplication.

Modular form 172062.2.a.e

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 172062e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
172062.bf2	172062e1	\([1, -1, 1, -457403, 118138155]\)	\(8194759433281/82837504\)	\(106981983047909376\)	\([]\)	\(2016000\)	\(2.0856\)	\(\Gamma_0(N)\)-optimal
172062.bf1	172062e2	\([1, -1, 1, -25460843, -49441119285]\)	\(1413378216646643521/49232902384\)	\(63582716449839738096\)	\([]\)	\(10080000\)	\(2.8904\)