Elliptic curve isogeny class with Cremona label 377520ev (LMFDB label 377520.ev)

• Label: 377520ev
• Number of curves: $4$
• Conductor: $377520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 377520ev have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 377520ev do not have complex multiplication.

Modular form 377520.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 377520ev

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
377520.ev4	377520ev1	\([0, 1, 0, 20409, 81684]\)	\(33165879296/19278675\)	\(-546453580186800\)	\([2]\)	\(1105920\)	\(1.5173\)	\(\Gamma_0(N)\)-optimal
377520.ev3	377520ev2	\([0, 1, 0, -81836, 572460]\)	\(133649126224/77000625\)	\(34921293881760000\)	\([2, 2]\)	\(2211840\)	\(1.8639\)
377520.ev1	377520ev3	\([0, 1, 0, -931256, 344757444]\)	\(49235161015876/137109375\)	\(248727164400000000\)	\([2]\)	\(4423680\)	\(2.2105\)
377520.ev2	377520ev4	\([0, 1, 0, -868336, -310566940]\)	\(39914580075556/172718325\)	\(313324593720652800\)	\([2]\)	\(4423680\)	\(2.2105\)