Elliptic curve isogeny class with Cremona label 84700bb (LMFDB label 84700.g)

• Label: 84700bb
• Number of curves: $2$
• Conductor: $84700$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 84700bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 84700bb do not have complex multiplication.

Modular form 84700.2.a.bb

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 84700bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
84700.g2	84700bb1	\([0, 1, 0, 5042, 402213]\)	\(1280/7\)	\(-77505793750000\)	\([]\)	\(243000\)	\(1.3472\)	\(\Gamma_0(N)\)-optimal
84700.g1	84700bb2	\([0, 1, 0, -297458, 62414713]\)	\(-262885120/343\)	\(-3797783893750000\)	\([]\)	\(729000\)	\(1.8965\)