Elliptic curve isogeny class with LMFDB label 305760.et (Cremona label 305760et)

• Label: 305760.et
• Number of curves: $4$
• Conductor: $305760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 305760.et have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 305760.et do not have complex multiplication.

Modular form 305760.2.a.et

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 305760.et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
305760.et1	305760et2	\([0, 1, 0, -11148496, 14319428780]\)	\(2543984126301795848/909361981125\)	\(54776590191296064000\)	\([2]\)	\(14155776\)	\(2.7567\)
305760.et2	305760et4	\([0, 1, 0, -5758496, -5211309720]\)	\(350584567631475848/8259273550125\)	\(497507980236111936000\)	\([2]\)	\(14155776\)	\(2.7567\)
305760.et3	305760et1	\([0, 1, 0, -797246, 154778280]\)	\(7442744143086784/2927948765625\)	\(22046095636929000000\)	\([2, 2]\)	\(7077888\)	\(2.4102\)	\(\Gamma_0(N)\)-optimal
305760.et4	305760et3	\([0, 1, 0, 2556559, 1120003359]\)	\(3834800837445824/3342041015625\)	\(-1610497161000000000000\)	\([2]\)	\(14155776\)	\(2.7567\)