Elliptic curve isogeny class with LMFDB label 135300.i (Cremona label 135300w)

• Label: 135300.i
• Number of curves: $2$
• Conductor: $135300$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 135300.i have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(41\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 135300.i do not have complex multiplication.

Modular form 135300.2.a.i

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 135300.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
135300.i1	135300w2	\([0, -1, 0, -227908, -41833688]\)	\(-327298742232784/284299125\)	\(-1137196500000000\)	\([]\)	\(684288\)	\(1.8151\)
135300.i2	135300w1	\([0, -1, 0, 3092, -253688]\)	\(817036976/7367085\)	\(-29468340000000\)	\([]\)	\(228096\)	\(1.2658\)	\(\Gamma_0(N)\)-optimal