Elliptic curve isogeny class with Cremona label 358974bj (LMFDB label 358974.bj)

• Label: 358974bj
• Number of curves: $2$
• Conductor: $358974$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 358974bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 358974bj do not have complex multiplication.

Modular form 358974.2.a.bj

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 358974bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
358974.bj2	358974bj1	\([1, -1, 0, -26717112, 24950049088]\)	\(24591016773082896625/11097062309363712\)	\(951751988769427556401152\)	\([2]\)	\(48660480\)	\(3.2963\)	\(\Gamma_0(N)\)-optimal
358974.bj1	358974bj2	\([1, -1, 0, -360889272, 2637574830400]\)	\(60607987148648054544625/35377817158176768\)	\(3034218147104064823676928\)	\([2]\)	\(97320960\)	\(3.6429\)