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

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

Rank

The elliptic curves in class 305760ev 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.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 305760.2.a.ev

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 305760ev

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
305760.ev3	305760ev1	\([0, 1, 0, -19126, -480376]\)	\(102766285504/46580625\)	\(350730492840000\)	\([2, 2]\)	\(1179648\)	\(1.4860\)	\(\Gamma_0(N)\)-optimal
305760.ev2	305760ev2	\([0, 1, 0, -152896, 22635080]\)	\(6562309703048/106640625\)	\(6423635400000000\)	\([2]\)	\(2359296\)	\(1.8326\)
305760.ev4	305760ev3	\([0, 1, 0, 66624, -3533076]\)	\(542939080312/404852175\)	\(-24386792210726400\)	\([2]\)	\(2359296\)	\(1.8326\)
305760.ev1	305760ev4	\([0, 1, 0, -258001, -50500801]\)	\(3941317078336/2340975\)	\(1128093154406400\)	\([2]\)	\(2359296\)	\(1.8326\)