Elliptic curve isogeny class with Cremona label 388080ix (LMFDB label 388080.ix)

• Label: 388080ix
• Number of curves: $4$
• Conductor: $388080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 388080ix have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388080ix do not have complex multiplication.

Modular form 388080.2.a.ix

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 388080ix

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388080.ix4	388080ix1	\([0, 0, 0, 70413, -58777166]\)	\(109902239/4312000\)	\(-1514797112328192000\)	\([2]\)	\(5308416\)	\(2.1683\)	\(\Gamma_0(N)\)-optimal
388080.ix2	388080ix2	\([0, 0, 0, -1905267, -968775374]\)	\(2177286259681/105875000\)	\(37193679097344000000\)	\([2]\)	\(10616832\)	\(2.5149\)
388080.ix3	388080ix3	\([0, 0, 0, -635187, 1607708914]\)	\(-80677568161/3131816380\)	\(-1100200929676746670080\)	\([2]\)	\(15925248\)	\(2.7177\)
388080.ix1	388080ix4	\([0, 0, 0, -24837267, 47383523026]\)	\(4823468134087681/30382271150\)	\(10673232051018584678400\)	\([2]\)	\(31850496\)	\(3.0642\)