Elliptic curve isogeny class with Cremona label 300762de (LMFDB label 300762.de)

• Label: 300762de
• Number of curves: $2$
• Conductor: $300762$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 300762de have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 300762de do not have complex multiplication.

Modular form 300762.2.a.de

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 300762de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
300762.de1	300762de1	\([1, -1, 1, -27572, 247475]\)	\(27027009001/15349092\)	\(1316432081712132\)	\([2]\)	\(2654208\)	\(1.5910\)	\(\Gamma_0(N)\)-optimal
300762.de2	300762de2	\([1, -1, 1, 109138, 1887995]\)	\(1676253304439/988531038\)	\(-84782472617363598\)	\([2]\)	\(5308416\)	\(1.9376\)