Elliptic curve isogeny class with LMFDB label 457776.dd (Cremona label 457776dd)

• Label: 457776.dd
• Number of curves: $4$
• Conductor: $457776$
• CM: no
• Rank: $1$

Elliptic curves in class 457776.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
457776.dd1	457776dd3	\([0, 0, 0, -690599542755, -220895843126453534]\)	\(505384091400037554067434625/815656731648\)	\(58787965324907450474692608\)	\([2]\)	\(1911029760\)	\(5.1000\)
457776.dd2	457776dd4	\([0, 0, 0, -690592884195, -220900315730478878]\)	\(-505369473241574671219626625/20303219722982711328\)	\(-1463342274693297285835943566245888\)	\([2]\)	\(3822059520\)	\(5.4466\)
457776.dd3	457776dd1	\([0, 0, 0, -8549924835, -301220064781598]\)	\(959024269496848362625/11151660319506432\)	\(803749168910445738977837187072\)	\([2]\)	\(637009920\)	\(4.5507\)	\(\Gamma_0(N)\)-optimal^*
457776.dd4	457776dd2	\([0, 0, 0, -1731559395, -768415828403486]\)	\(-7966267523043306625/3534510366354604032\)	\(-254747695685605620811640887836672\)	\([2]\)	\(1274019840\)	\(4.8973\)

^*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 457776.dd1.

Rank

The elliptic curves in class 457776.dd have rank \(1\).

Complex multiplication

The elliptic curves in class 457776.dd do not have complex multiplication.

Modular form 457776.2.a.dd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.