Elliptic curve isogeny class with Cremona label 363090ds (LMFDB label 363090.ds)

• Label: 363090ds
• Number of curves: $4$
• Conductor: $363090$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 363090ds have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 363090ds do not have complex multiplication.

Modular form 363090.2.a.ds

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 363090ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
363090.ds4	363090ds1	\([1, 0, 1, -696463, 234746306]\)	\(-317562142497484249/18670942617600\)	\(-2196617728018022400\)	\([2]\)	\(7864320\)	\(2.2754\)	\(\Gamma_0(N)\)-optimal
363090.ds3	363090ds2	\([1, 0, 1, -11296143, 14612152258]\)	\(1354958399265695661529/4304795040000\)	\(506454831660960000\)	\([2, 2]\)	\(15728640\)	\(2.6219\)
363090.ds1	363090ds3	\([1, 0, 1, -180738143, 935224426658]\)	\(5549896908024170183373529/56019600\)	\(6590649920400\)	\([2]\)	\(31457280\)	\(2.9685\)
363090.ds2	363090ds4	\([1, 0, 1, -11449023, 14196257506]\)	\(1410719602237262088409/76269550743750000\)	\(8973036375451443750000\)	\([2]\)	\(31457280\)	\(2.9685\)