Elliptic curve isogeny class with LMFDB label 305552.e (Cremona label 305552e)

• Label: 305552.e
• Number of curves: $2$
• Conductor: $305552$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 305552.e have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(113\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 305552.e do not have complex multiplication.

Modular form 305552.2.a.e

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 305552.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
305552.e1	305552e1	\([0, 1, 0, -5464, 136020]\)	\(912673/113\)	\(2234078892032\)	\([2]\)	\(442368\)	\(1.0994\)	\(\Gamma_0(N)\)-optimal
305552.e2	305552e2	\([0, 1, 0, 8056, 714676]\)	\(2924207/12769\)	\(-252450914799616\)	\([2]\)	\(884736\)	\(1.4460\)