Elliptic curve isogeny class with LMFDB label 378560.ex (Cremona label 378560ex)

• Label: 378560.ex
• Number of curves: $4$
• Conductor: $378560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 378560.ex have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 378560.ex do not have complex multiplication.

Modular form 378560.2.a.ex

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 378560.ex

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
378560.ex1	378560ex3	\([0, 0, 0, -4290572, 3256375824]\)	\(6903498885921/374712065\)	\(474130302304409354240\)	\([2]\)	\(11010048\)	\(2.7233\)
378560.ex2	378560ex2	\([0, 0, 0, -775372, -198362736]\)	\(40743095121/10144225\)	\(12835680820402585600\)	\([2, 2]\)	\(5505024\)	\(2.3768\)
378560.ex3	378560ex1	\([0, 0, 0, -721292, -235764464]\)	\(32798729601/3185\)	\(4030041073909760\)	\([2]\)	\(2752512\)	\(2.0302\)	\(\Gamma_0(N)\)-optimal
378560.ex4	378560ex4	\([0, 0, 0, 1874548, -1259390704]\)	\(575722725759/874680625\)	\(-1106750029922467840000\)	\([2]\)	\(11010048\)	\(2.7233\)