# Properties

 Label 51600.ct Number of curves $4$ Conductor $51600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.ct1 51600u4 $$[0, 1, 0, -6192008, -5932620012]$$ $$820480625548035842/5805$$ $$185760000000$$ $$[2]$$ $$811008$$ $$2.2167$$
51600.ct2 51600u3 $$[0, 1, 0, -414008, -79128012]$$ $$245245463376482/57692266875$$ $$1846152540000000000$$ $$[2]$$ $$811008$$ $$2.2167$$
51600.ct3 51600u2 $$[0, 1, 0, -387008, -92790012]$$ $$400649568576484/33698025$$ $$539168400000000$$ $$[2, 2]$$ $$405504$$ $$1.8701$$
51600.ct4 51600u1 $$[0, 1, 0, -22508, -1665012]$$ $$-315278049616/114259815$$ $$-457039260000000$$ $$[2]$$ $$202752$$ $$1.5235$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 51600.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.