Elliptic curve isogeny class with Cremona label 28350cm (LMFDB label 28350.cl)

• Label: 28350cm
• Number of curves: $2$
• Conductor: $28350$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 28350cm have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28350cm do not have complex multiplication.

Modular form 28350.2.a.cm

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 28350cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28350.cl1	28350cm1	\([1, -1, 1, -1955, 34147]\)	\(-1812792825/25088\)	\(-11430720000\)	\([3]\)	\(23328\)	\(0.73631\)	\(\Gamma_0(N)\)-optimal
28350.cl2	28350cm2	\([1, -1, 1, 7045, 167347]\)	\(1047929175/941192\)	\(-34735279005000\)	\([]\)	\(69984\)	\(1.2856\)