Elliptic curve isogeny class with LMFDB label 466752.bu (Cremona label 466752bu)

• Label: 466752.bu
• Number of curves: $4$
• Conductor: $466752$
• CM: no
• Rank: $1$

Elliptic curves in class 466752.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
466752.bu1	466752bu3	\([0, -1, 0, -160617801217, 24776466871606177]\)	\(1748094148784980747354970849498497/887694600425282263291392\)	\(232703813333885193628258664448\)	\([2]\)	\(1815478272\)	\(4.9677\)	\(\Gamma_0(N)\)-optimal^*
466752.bu2	466752bu4	\([0, -1, 0, -21971478017, -689374449575007]\)	\(4474676144192042711273397261697/1806328356954994499451382272\)	\(473518140805610078064183154311168\)	\([2]\)	\(1815478272\)	\(4.9677\)
466752.bu3	466752bu2	\([0, -1, 0, -10092914177, 382734832655265]\)	\(433744050935826360922067531137/9612122270219882316693504\)	\(2519760180404520830027301912576\)	\([2, 2]\)	\(907739136\)	\(4.6211\)	\(\Gamma_0(N)\)-optimal^*
466752.bu4	466752bu1	\([0, -1, 0, 57301503, 18331939527585]\)	\(79374649975090937760383/553856914190911653543936\)	\(-145190266913662344506621558784\)	\([2]\)	\(453869568\)	\(4.2746\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 466752.bu1.

Rank

The elliptic curves in class 466752.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 466752.bu do not have complex multiplication.

Modular form 466752.2.a.bu

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.