Elliptic curve isogeny class with Cremona label 297660ba (LMFDB label 297660.ba)

• Label: 297660ba
• Number of curves: $2$
• Conductor: $297660$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 297660ba have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 297660ba do not have complex multiplication.

Modular form 297660.2.a.ba

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 297660ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
297660.ba2	297660ba1	\([0, 1, 0, 14964, 2695284]\)	\(817036976/7367085\)	\(-3341117560239360\)	\([]\)	\(1140480\)	\(1.6600\)	\(\Gamma_0(N)\)-optimal
297660.ba1	297660ba2	\([0, 1, 0, -1103076, 445886340]\)	\(-327298742232784/284299125\)	\(-128935229999136000\)	\([]\)	\(3421440\)	\(2.2093\)