Elliptic curve isogeny class with Cremona label 308550ez (LMFDB label 308550.ez)

• Label: 308550ez
• Number of curves: $4$
• Conductor: $308550$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 308550ez have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 308550ez do not have complex multiplication.

Modular form 308550.2.a.ez

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 308550ez

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308550.ez3	308550ez1	\([1, 0, 1, -25045551, 43407358498]\)	\(62768149033310713/6915442583808\)	\(191423880925210692000000\)	\([2]\)	\(58982400\)	\(3.2008\)	\(\Gamma_0(N)\)-optimal
308550.ez2	308550ez2	\([1, 0, 1, -94983551, -309779541502]\)	\(3423676911662954233/483711578981136\)	\(13389446383928129270250000\)	\([2, 2]\)	\(117964800\)	\(3.5474\)
308550.ez4	308550ez3	\([1, 0, 1, 154941949, -1664875602502]\)	\(14861225463775641287/51859390496937804\)	\(-1435501151377275515500687500\)	\([2]\)	\(235929600\)	\(3.8939\)
308550.ez1	308550ez4	\([1, 0, 1, -1463917051, -21558365328502]\)	\(12534210458299016895673/315581882565708\)	\(8735508679062316096687500\)	\([2]\)	\(235929600\)	\(3.8939\)