Elliptic curve isogeny class with LMFDB label 304200.eb (Cremona label 304200eb)

• Label: 304200.eb
• Number of curves: $2$
• Conductor: $304200$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 304200.eb have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 304200.eb do not have complex multiplication.

Modular form 304200.2.a.eb

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 304200.eb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
304200.eb1	304200eb2	\([0, 0, 0, -1939275, -696998250]\)	\(530604/169\)	\(256896444503088000000\)	\([2]\)	\(8257536\)	\(2.6201\)
304200.eb2	304200eb1	\([0, 0, 0, 342225, -74148750]\)	\(11664/13\)	\(-4940316240444000000\)	\([2]\)	\(4128768\)	\(2.2735\)	\(\Gamma_0(N)\)-optimal