Elliptic curve isogeny class with Cremona label 17850bf (LMFDB label 17850.bi)

• Label: 17850bf
• Number of curves: $4$
• Conductor: $17850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 17850bf have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17850bf do not have complex multiplication.

Modular form 17850.2.a.bf

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 17850bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17850.bi3	17850bf1	\([1, 1, 1, -449938, 116032031]\)	\(-644706081631626841/347004000000\)	\(-5421937500000000\)	\([2]\)	\(221184\)	\(1.9683\)	\(\Gamma_0(N)\)-optimal
17850.bi2	17850bf2	\([1, 1, 1, -7199938, 7433032031]\)	\(2641739317048851306841/764694000\)	\(11948343750000\)	\([2]\)	\(442368\)	\(2.3148\)
17850.bi4	17850bf3	\([1, 1, 1, 365687, 472207031]\)	\(346124368852751159/6361262220902400\)	\(-99394722201600000000\)	\([2]\)	\(663552\)	\(2.5176\)
17850.bi1	17850bf4	\([1, 1, 1, -7314313, 7184527031]\)	\(2769646315294225853641/174474906948464640\)	\(2726170421069760000000\)	\([2]\)	\(1327104\)	\(2.8642\)