# Properties

 Label 51600.d Number of curves $2$ Conductor $51600$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.d1 51600bx2 $$[0, -1, 0, -66310408, 207857731312]$$ $$503835593418244309249/898614000000$$ $$57511296000000000000$$ $$$$ $$5806080$$ $$3.0499$$
51600.d2 51600bx1 $$[0, -1, 0, -4102408, 3317827312]$$ $$-119305480789133569/5200091136000$$ $$-332805832704000000000$$ $$$$ $$2903040$$ $$2.7033$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.d do not have complex multiplication.

## Modular form 51600.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 4q^{11} - 4q^{13} - 4q^{17} - 4q^{19} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 