Elliptic curve isogeny class with LMFDB label 145200.e (Cremona label 145200js)

• Label: 145200.e
• Number of curves: $2$
• Conductor: $145200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 145200.e have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 145200.e do not have complex multiplication.

Modular form 145200.2.a.e

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 145200.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145200.e1	145200js2	\([0, -1, 0, -4115008, 98300512]\)	\(102129622/59049\)	\(4455502502587488000000\)	\([2]\)	\(10137600\)	\(2.8435\)
145200.e2	145200js1	\([0, -1, 0, -2784008, -1781071488]\)	\(63253004/243\)	\(9167700622608000000\)	\([2]\)	\(5068800\)	\(2.4969\)	\(\Gamma_0(N)\)-optimal