Elliptic curve isogeny class with Cremona label 149454p (LMFDB label 149454.ce)

• Label: 149454p
• Number of curves: $2$
• Conductor: $149454$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 149454p have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(19\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 149454p do not have complex multiplication.

Modular form 149454.2.a.p

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 149454p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
149454.ce1	149454p1	\([1, -1, 1, -428765, -106135707]\)	\(1743381413738875/33697824768\)	\(168496234081026048\)	\([2]\)	\(1728000\)	\(2.0983\)	\(\Gamma_0(N)\)-optimal
149454.ce2	149454p2	\([1, -1, 1, 8995, -312933531]\)	\(16098453125/8460457579008\)	\(-42304073051589170688\)	\([2]\)	\(3456000\)	\(2.4448\)