Elliptic curve isogeny class with LMFDB label 400554.fh (Cremona label 400554fh)

• Label: 400554.fh
• Number of curves: $4$
• Conductor: $400554$
• CM: no
• Rank: $1$

Elliptic curves in class 400554.fh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
400554.fh1	400554fh4	\([1, -1, 1, -239303759, -1424800695625]\)	\(86129359107301290313/9166294368\)	\(161292753768013404768\)	\([2]\)	\(70778880\)	\(3.3052\)
400554.fh2	400554fh2	\([1, -1, 1, -14993519, -22143902857]\)	\(21184262604460873/216872764416\)	\(3816155578862407689216\)	\([2, 2]\)	\(35389440\)	\(2.9586\)
400554.fh3	400554fh3	\([1, -1, 1, -3757199, -54571922377]\)	\(-333345918055753/72923718045024\)	\(-1283186730239219379952224\)	\([2]\)	\(70778880\)	\(3.3052\)
400554.fh4	400554fh1	\([1, -1, 1, -1676399, 276800375]\)	\(29609739866953/15259926528\)	\(268518059008802684928\)	\([2]\)	\(17694720\)	\(2.6121\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 400554.fh1.

Rank

The elliptic curves in class 400554.fh have rank \(1\).

Complex multiplication

The elliptic curves in class 400554.fh do not have complex multiplication.

Modular form 400554.2.a.fh

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.