Elliptic curve isogeny class with Cremona label 123210cu (LMFDB label 123210.ch)

• Label: 123210cu
• Number of curves: $2$
• Conductor: $123210$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 123210cu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 123210cu do not have complex multiplication.

Modular form 123210.2.a.cu

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 123210cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
123210.ch2	123210cu1	\([1, -1, 1, -1027522373, 16915218747581]\)	\(-64144540676215729729/28962038218752000\)	\(-54171017744596788232323072000\)	\([]\)	\(86676480\)	\(4.2202\)	\(\Gamma_0(N)\)-optimal
123210.ch1	123210cu2	\([1, -1, 1, -90732287813, 10519421525885117]\)	\(-44164307457093068844199489/1823508000000000\)	\(-3410715899182000788000000000\)	\([]\)	\(260029440\)	\(4.7695\)