Elliptic curve isogeny class with Cremona label 279300cs (LMFDB label 279300.cs)

• Label: 279300cs
• Number of curves: $4$
• Conductor: $279300$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 279300cs have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 279300cs do not have complex multiplication.

Modular form 279300.2.a.cs

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 279300cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
279300.cs4	279300cs1	\([0, 1, 0, -1496133, -704809512]\)	\(12592337649664/1315845\)	\(38701962101250000\)	\([2]\)	\(4976640\)	\(2.2149\)	\(\Gamma_0(N)\)-optimal
279300.cs3	279300cs2	\([0, 1, 0, -1612508, -588900012]\)	\(985329269584/252434475\)	\(118794654197100000000\)	\([2]\)	\(9953280\)	\(2.5614\)
279300.cs2	279300cs3	\([0, 1, 0, -3260133, 1235810988]\)	\(130287139815424/52926616125\)	\(1556690865122531250000\)	\([2]\)	\(14929920\)	\(2.7642\)
279300.cs1	279300cs4	\([0, 1, 0, -45271508, 117187205988]\)	\(21804712949838544/8680921875\)	\(4085207110687500000000\)	\([2]\)	\(29859840\)	\(3.1107\)