Elliptic curve isogeny class with Cremona label 5880h (LMFDB label 5880.l)

• Label: 5880h
• Number of curves: $4$
• Conductor: $5880$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 5880h have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5880h do not have complex multiplication.

Modular form 5880.2.a.h

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 5880h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5880.l3	5880h1	\([0, -1, 0, -1371575, 618611652]\)	\(151591373397612544/32558203125\)	\(61287040631250000\)	\([4]\)	\(92160\)	\(2.2160\)	\(\Gamma_0(N)\)-optimal
5880.l2	5880h2	\([0, -1, 0, -1524700, 472101652]\)	\(13015144447800784/4341909875625\)	\(130770266869095840000\)	\([2, 2]\)	\(184320\)	\(2.5626\)
5880.l1	5880h3	\([0, -1, 0, -9928200, -11686082148]\)	\(898353183174324196/29899176238575\)	\(3602030781739120819200\)	\([2]\)	\(368640\)	\(2.9092\)
5880.l4	5880h4	\([0, -1, 0, 4428800, 3251195452]\)	\(79743193254623804/84085819746075\)	\(-10130035309881321139200\)	\([2]\)	\(368640\)	\(2.9092\)