Elliptic curve isogeny class with LMFDB label 306850.i (Cremona label 306850i)

• Label: 306850.i
• Number of curves: $2$
• Conductor: $306850$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 306850.i have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(17\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 306850.i do not have complex multiplication.

Modular form 306850.2.a.i

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 306850.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
306850.i1	306850i1	\([1, 0, 1, -67876, -5901102]\)	\(47045881/6800\)	\(4998624856250000\)	\([2]\)	\(2322432\)	\(1.7376\)	\(\Gamma_0(N)\)-optimal
306850.i2	306850i2	\([1, 0, 1, 112624, -31893102]\)	\(214921799/722500\)	\(-531103890976562500\)	\([2]\)	\(4644864\)	\(2.0842\)